Gerard ’t Hooft: A diferent string theory

The first oe paper is LOCALLY FINITE MODEL FOR GRAVITY written by Gerard ’t Hooft. If by some casual you dont know who ´t hoof is just to say that he has a nobel prize by proving that the gauge theories, wich are the basic ingredient, of the standard model, are renormalizable. A few physicists I know consider him the last greater phyisicist (Steven Weinberg would be considered slighly earlier in time). ON the other hand be sure that Lubos Motl is not among his fans ;-). Ok, let´s leave sociology and go into physic. The abstract of the paper is this:

Matter interacting classically with gravity in 3+1 dimensions usually gives
rise to a continuum of degrees of freedom, so that, in any attempt to quantize
the theory, ultraviolet divergences are nearly inevitable. Here, we investigate
matter of a form that only displays a finite number of degrees of freedom
in compact sections of space-time. In finite domains, one has only exact,
analytic solutions. This is achieved by limiting ourselves to straight pieces of
string, surrounded by locally flat sections of space-time. Globally, however,
the model is not finite, because solutions tend to generate infinite fractals.
The model is not (yet) quantized, but could serve as an interesting setting
for analytical approaches to classical general relativity, as well as a possible
stepping stone for quantum models. Details of its properties are explained,
but some problems remain unsolved, such as a complete description of the
most violent interactions, which can become quite complex.

The paper begins with some considerations about 2+1 dimensions and the role of pont partile matter as source of curvature, in the form of a wedge in space time. Inspired by that view he considers the extension of this to 3+1 dimensions. The role of the point particles are now strings. Why? Simply because the aditional dimension is perpendicular to the others and so a point becomes an infinite string. In principle it could look a bit arbitrary, and not general. But the idea seems to consider the space-time sourruounding that infinite strings.

He writes the energy momentun tensor for that strings (well known for people aware of cosmic strings). Later he considers moving and interacting strings. In considering this he concerns about holonomy so maybe the reader would consult something about this topic if he does´nt know it previously. The wikipedia entry is specially good about the topic so it could be a quick start guide. The very quick idea of homotopy is to consider a map betwen parallel transport of vectors around a closed curve and the group associated to the bundle (wich defines the very concept of paralell transpoort).

Afther that he considers interactions of strings. The first claim is as a resoult of interactions, connections, he cant´consider infinite strings alone anymore. Diferent types of collisions are analized. He cnsiders vaious posibilities and takes care about some possible issues (for example, rotating strings would create spacetimes with closed timelike curves as is well known since the work of Gott). I am not sure of how much of this work would intersect with the well stablished resoults about networks of cosmic strings (gauge or superstring ones). It would be fine if some reader would know it and could say something about it.

The final conclusion he claims is that he can get all the degrees of freedom of gravity by pieces of straight strings. In this way he could study gravity just from this. Seemengly this is somewhat similar to Regge calculus (a discretized aproach to quantum gravity)using strings instead of points in the nodes. He also says that in this sense is just the opposite to some papers triying to get matter from ure gravity (in a clear reference to Smollin program in the octopy). In the paper a quantizaion of the model is not made, that is announced for a future paper. About that paper he says that he will not follow traditional quantiztion proceduers based in lagrangian mechanisms,partially because the model seems not to admit a Lagrangian formulation). AS an advance a claim is made that the theory will not have ultraviolete divergences but possibly will have problems with infrared regime.

Well, I still have to re-read carefully some pieces of the paper, and a definite juice will only be possible when the paper on quantization would be available. Also it would be interesting to see how it is recived by the mainstream physic comunity. For example Sean carroll has announced that he will speak about the paper (it is how I knew about it´s existence). And, I guess that also Lubos Motl will have something to say, given his aparent animosity against t' hoof (maybe because he has sometimes soped favourably about the LQG comunity). Personally I consider ’t Hooft a very interisting figure and I like to be aware of what he does, even if I don´t necesarilly agree with all his conclusions.

New, complementary, blog

As announced I have created an aditional blog inwordpress. The actual url is http://freelancescience.wordpress.com/.

The idea is to keep this blog for quantum gravity related stuf and the other for diferent aspects of physics, math, and, ocasionally, another sciences. A separate interest is to see how well it works the LaTeX functionality of wordpress. If it works fine, and blogspot refuses to allow LaTeX, I would consider the posibility to migrate this blog there (afther all they have facilities to do so).

Advise, the other blog will have most of their entries in spanish, because of the expected target audience, if some non spanish speaker is particularly interested in seeing english entries he could let me a message and I would see what it can be done.

Fresh air for string theory

The very recent mounths seem to have brought great news for string theory. I´ll write in this post a brief guide to the relevant papers.

The first, cronologically, is this paper by Beasley, Heckman and Vafa. It is a paper where, for the first time, it is addressed the task of constructing phenomenology from F-theory. A second one is announced where the program started in thiw will be concluded. If 125 pages is more time of what you have available just now you can try to read a sinopsis in the Jackes Distler glog, concretelly here. Lubos also wrote his own comment, try to search for it in his blog ;-).

Maybe the reader has no too much familiarity with compactifications and similars. In that case, or even if he has, it would be recomendable the following paper Les houches lectures on constructing string vacua. The great point of that paper is that it covers in a single paper approach for many types of strings, and many types of vacua (compactifications, fluxes, etc).

Another very interesting topic are advances in M-theory and their interactions. A review explaing the topic can read here. Well, two papers have changed things and some people (yes, you are rgiht, Lubos) has told that it may be the beguining of a third string theory revolution. The papers in question are these:Gauge Symmetry and supersymmetry of Multiple M2-Branes and M2 to D2. You can read a brief description in Lubo´s or Distler´s blogs. I particularly recomend, if you are in a hurry, the one in Lubos blog because it is easier to understand.

Not enought reading? Well, there is a very recent paper in perturbabtive string theory. Concretely some where the four loop amplitude for string theory is explictely calculated. The author of the paper is Samuel Grushevsky and the actual paper is this

For the string heater readers I would recomend reading this paper by Smollin and all. They continuate their "ocutopussy program" where the try to get the standar model from spin networks of pure gravity. To be honnest, I don´t really think that approach is particularly viable, measured by the own standards of the LQG commnuity, but it is up the readers own judice to decide what is interesting or not.

To conclud simply to say that at last I found a great reference for the basics of the renormalization group, as well as in many other topics,the three volumes book of Steven Weinberg in quantum field theory. I had never tried to read that book because of it´s extension (and because, hey, I already had a reasonably good knowledge of the subject) but I must say that despite of ít´s extension it is so well written that one can read it fast. I hope to write soon a post about the subject of renormalization group theory, that could serve as an introduction to those who would want to follow the Martin reuter papers on the subject and the discusions on Distler blog on the particular.

Status of the blog

I have writen relatively few (here and in forums) in the las times. This doesn´t mean that I would have somewhatleft the physici, quite on the contrary.

Cronologicaly the first reason to stop me writng was to do a sistematic reading of Jackes Distler´s blog. That gave me a partial idea of what had been hapening in string theory and quantum gravity in general in the very last years. One of the things that one can learn there are that some of the discusions betwen the LQG comunity and the string comunity come from online discusions. Particularly it was interesting, concerning this "string wars" a post with around 100 answers about chirality in LQG. AS a consecuence of that reading I studied the chapter on chirality of he book "topology and quantum field theory" together with all the preliminars required for it (Sheave comology, some basic K theory and Atiyha singer theorem explianed in that framework, certinly not trivial things). I had readed some chapters of that book previously, but I practically had to reread them, together with some ampliations to get (aprt of the above mentioned) a, still far for finished, understanding of anlgebraic geometry. In fact that chapter, in my opinion, is far for complete, and maybe I will read in the future some of the available reviews. Anyway I think I got a decent idea of the arguments of Distler against the Smollin arguments. In fact i guess that a better defense could have been made of the case for LQG. As I understand the problem the reason why you can´t have chiral matter in LQG is that LQG is thinked by string people as some kind of latice theory. But in latice theries you can´t have chiral matter because of the period doulbing problem (there are many places to study an introduction to QFT on the latice. Perhaps my favourite one is the chapter of the Michio Kaku book on QFT). But the thing is that, as far as I undertand it the way the spin network is thinked (or wishefull thinked, who knows?)in LQG isn´t exactly a latice theory. In particular there is no topology in spin networks, or spinfoams for what matters, (LQG is a pre-topology theory)and It would evade the topological character whch make chirality a deep nature beyond their perturbative appearence in the famous triangle Feynman graph. But, certainly, if the LQG cmunity didn´t did that defense it probably means that I am loosing some point, that is, they are the experts, I have a reasonable knowledge of canonical LQG and, to a lesser extent, sin foams, but for sure I am not an expert.

Another thing that I learned, about the string wars, in Distler´s blog is that prt of it happened in the, sadly stopped, string coffee blog. I have the intention of reading it sistemathicallly also, but some things prevented me form doing it. For example reading comments about the Lisi´s E(8) theory I realized that what I had been teached about group theory in the course at the university was far from enought. I still think, as I expresed before that group theory aalone isn´t going to give answers to quntum gravity problems. But anyway It was obvious that I needed to learn better the subject. It was a very, very ugly task. As I have said in this blog my mathemathical formation is s mathemathician, rather than as phyisician, so for me the books of group theory for phyisic are somewht like a nightmare. In mathemathics a Lie group is a relatively easy thing to understand once you understand geomtery in manifolds. The definitions are elegant and natural. In physics the idea of continous groups, in the sense of calculus, and matrix groups seems rogught, and maybe even limited. But if at the level of the group the discrepances are relatively solvables at the level of the Lie algebra the problems row fast and it is almost an act of faith to belive that definitions ocf Cartan subalgebras, root vectors and almost everything are the same as stated in, for example, the book of Georgy (Lie algebras in particle physics) and in, for example, the book of Sattinger and Weaver (symmetry groups, geometry and physics, if I don´t remmeber bad the title) where they are introduced using notions of abstract álgebra (solvable ideals and thngs like that). An added problem is that mathemathicians interest in Lie groups seems to be the clasification of symmetric spaces more than in particle physic (although they also cover it, mainly the "wight fold way). Well, anyway I, at last, learned properly about the relation betwen ral and complex forms of a lie aalgebra and it´s consequences. One added problem with group theory, as teached by mathemathicians, is that they make a good cover of the clasification of Lie algebras, and give a quick tour in representation theory (including sinor representations of some algebras). But htey uses very, relatively, asic techniches. A physicans book, on the contrary, gives an in deep tratement on SU(n) wiht basic, as well as tensor methods and the younng Tableaux technicke. Those last ones, in particular, resoult that are also used in the representations of the Lorentz group, because of the litle grou and all that. Young Tableaux are not particularly difficoult to understand, basically a way to represent symmetric and antisymmetric part of a tensor products. So, when I found then in string theory books as a way to represent the particle content of the strings, I understood what was going on, but lacking calculational confidence (It was not teached in my course at the university and I just had readed previously the basic ideas) always maade me feel that that calculation of the string spectrum was "goup theory maguffery". I still think that it´s is not the best way to show the physic content of the string theories so I recmend to read the corresponding chapters in the books of Polyakov and Zweibach where one can get a more deep physical idea of what´s going on.

Another ugly part of group theory, this time restricted to physicians oriented books, is the choice of examples. Some books, for example the one of Miller, makes an extensive use of examples extracted from non relativistic quantum theory. Anthoer´s, the one of Georgy, focuses more on particle physics. In fact I can´t say for sure that it is a bad thin, but one can get lost with so many "phenomenology" and loose the common points. A separate problem is the Poincaré and Lorentz groups. I still have not totally clear how important is to care about irreducible representations, which are necesarilly infinite dimensinal, and why more aspects are done with finite dimensinal ones. Maybe the lecture of the techniche of the induced representation, whch I still didn´t do, clarify me some things. I also have no clear why exactly are important in general the casimir operators of a representation. And I still have a vague idea of the role of chaaracters of representaions for Lie groups. AS the reader can deduce group theory has many aspects and it is easy to get a false idea tht some knows properly it. Fourtounately I never have felt that a not perfect understanding of some particular aspects of group theroy forbids me to understand the ideas of physic. In fact one thing that always had intrigued me, the way quarks were assigned charge was not rellated (as I thought) to conserved charges ia the Noether theorem but comes from the pauli principle (for quantum numbers difernet from spin) which dictates some prticular choice of the representation (assoiciated vector bundle in the language of geometry of fiber bundles).

But the previous things have not been my main, and more difficoult concern, these last times. Afther all my basic in math is solid (or at lest I thnk so) and, beyond the problem of tradution betwen pure math texts and physicans math texts I had not deep problmes of understanding. The thing which more problems gave tome is the renormalization group. I haad previously mentioned an entry of Distler about the modern renormalization group and it´s relation to the try of Reuters to find a non perturbative way to get a quantum gravity along the more traditinal lines of QFT. Well, Distler, and also Lubos, gave some ideas of what´s was ging there, and remarked how important it was to know the exact renormalization group equations. In fact Distler did recently two new posts about the topic. Well, that has suposed a big problem for me. I knew reasonably well the old perturbabative renormalization and the renormalizaation group of Callan-Symanzisk, and it´s role for the calculation of the running coupling constants. I also could get an intuitive idea of what is a releant, irrelevant or marginal operator. Afhter all similar cncepts are used in conformal field theory. But one thing is to have a vague idea aand another a proper understanding, so I went to the string wiki and pursued the review articles. And I got totally lost. The ultimate reason for that is that that ideas of renormalization group come from condensed matter (il.e. statiticall physic). And that is a very bad new for me. My knowledge of termodinamics and statistical physic was, well, er...average ;-). I mean, I had a right understanding of the microcanonical ensemble, whch allowed me to undersandthe meaning of entropy. I understod the role of the other ensambles and that you could get termodynamics from statisticall mechanics (and that point not quite well). The problem is that I never had understood the utility of thermodinamics (in my first contact with it was tacitally assumed that I already knew it and the focous was in it´s relation to statisticall mechanics, pitty tht I never had been teached it). Well, no problem, what really was needed was to learn statistichal mechanics, and to calculate partition functions, classical and quantum. I got used to learn about fery and bose statistic and, to be honest, not too much more. Beeing a "pure theoretic" that never worried me too much. I could, more or less follow the basic ideas I needed to u nderstand in solid state physic and I neveer cared too much. In fact I gained some better understanding of some aspectos of termodinamics, including a somewhat non stndar aspects, Ossanger relations, reading about thermodinamics in biologic procces. I also had some very vague notios about phase transitions, in the Erenfest classification.

Well, all of that tottally insuifient. Once I realized that by reading the availabe reviews I was going to nowere I decided to follow the ling way and to relearn all the thermodinamcic and statistical l hysic from the beguining. Afther that I readed the chapters of the Kerson Huang book on phase transition and renormalization group. There I learned about things such like "kadanof blocking", the meaning of fixed points and all that. But still I felt thaat I was lacking many detaills. I tried to read agian some reviews and I got more ideas, but still not eonguht. I learned that, beyond the work of Wilson, there were tow "exact renormalization group equations". The Wegner-Hougthon and the Polchinsky ones. I even tried to read the original article of Polchinsky and besides ewin advised that he was able to proof the renormalizability of the interacting sclar theory without using topology of Feynman graphs and the Weinberg therem I didn´t understand anything. Somewhat desesperated I readed the nobel price acceptance article of Wilson and I got a better idea of what it would be the path to follow. I went for a book of renormalization group and phase transitions for condensed matter phisicans. Concretely I got "lectures on phase transitions and the renormalization group" by Nigel Goldenfeld. AS I had readed in the Huang book the basic ideas of phase transitions I went directlly to the chapters on the renormalization group. I didn´t understand all the points, particularly I got a bit lost in the 10th chapter abut anomalous dimensions. But, in general, I got, at last, a felling that I am in the right waay. A problem (probably the only one in a very well written and clear book) is that it doesn´t use field theoretic (i.e. path integral) technckes. For that particular are recomended tow books, one of Collins "renormaliztion" and one form Zin-Justin "renormalization group and critical phenomena". To be honnest, afhter all this statistichal mechanics I was dissapointed to have to read just another book. So I tried to read agian one of the review articles, and this time, at last, I understood the basic ideas, and some of the detaills. Also I have beguined to catch the detaill of the relations betwen the old and new renormalization group equations. Not surprsingly I learned that there were some diferences in the aspects of the renormalization group that interest to condensed matter physics (local ones, basically to calculate critical exponents) and the aspects usefull for an particle physis (the so called global renormalization group). Althought seemenly not essenciall I decided to read the first chapters of the goldenfeld book in general phase transition theory. I must say that I am finding it a very good idea because It clarfies the concepts a lot better that the Kerson Huang´s book. Also, beeing so well writen, seems not to be a very mcuh time consuming task.

Afther that I plain to read a book (fortunately short) about conformall field theory oriented minlly to statisticall physic. I understand CFT as applied to string theory, but I guess that reading that book I am going to get a cleare ideas of many aspects, which I now understand at the formal levl, but, probably, have some subleties that I am missing now.

And while I passed all this time triying to fill some gaps Mr Lubos Motl has recommeded as "imprescindible" not one, but two articles in string theory, of 100+ pages any. And one of the articles is just the first part of another (probalby of similar size). Er, fine, it´s good to do quantum gravity, isn´t it? xD.

Anyway, if there is out there some lector who find that my actual publication rate in this blog is not fast enought I have good news for him/her. I have another journal, in livejournal, where I have published about other topics than quantum gravity. The level, and thematic, of that journal is to wide, it includes music, cinema, sci-fi and some more topics. Sitll it is mainly a physics/mathematics journal and there are some not too bad posts in this areas. I have decided to open anthoer blog (maybe in wordpress) where I will collect the better of that articles and post new ones. I prefer to rserve this blog exclusively for quantum gravity, and I guess the reader interested in physics and maths will be glad not to have to read posts of topic triying to search interesting things (I personally find annoying to read physics journals where most of the posts are not related to physic). I am sad to say, for english readers, that in that blog all, or almost all, entries will be in spanish, sorry for te inconvenience.

P.S. I have seen just now an answer in the last post that I had missed, I´ll try to answer it as son as possible.

¿Por que el universo tiene 3 + 1 dimensiones? (Parte 1)

Esta pregunta tiene una respuesta fácil, porque experimentalmente es lo que se observa.

La problemática surge dentro del marco de las teorias de cuerdas, que tienen cómo requisito (salvo en versiones harto polémicas cómo las cuerdas de Liouville u otras también bastante discutibles, cómo las cuerdas supercríticas) que esten formuladas en 10 (u 11 para la teoria M) dimensiones.

Aquí he hablado de soluciones "ad-hoc", cómo la compactificación de las dimensiones extra. También he mencionado las soluciones basadas en "warped geometries", he discutido con más detalle (eso sí, en inglés, por eso en este post repito cosas que he explicado antes en inglés, por si algun lector no conociese ese idioma) en el contexto de la teoria de Horava-Witten, o teoria M-heterótica. Este mes la autora de la teoria de los warped universes (junto a Kunrum Sumdrum) Lisa Randall tiene un nuevo paper, esta vez en colaboración con Andreas Karch, que pretende explicar de una manera "nautral" cómo el universo puede haber llegado a una configuración en las que sólo 3 de las 9 dimensiones espaciales tienen un tamaño macroscópico.

Para entender las argumentaciones que hace primero debo explicar algunas cosas básicaas de teoria de cuerdas. Aparte de los objetos más fundamentales, las cuerdas, la teoria requiere la posibilidad de que existan otros objetos extensos, las p-branas (p es la dimension del objeto extenso). Una 1-brana sería un objeto de dimensión 1, geometricamente una curva (real, nada de complejos, sí en algun momento usara dimensiones complejas lo indicaría explicitamente, por defecto debe entenderse siempre que estoy en el cuerpo de los reales), por ejemplo una cuerda sería un caso particular de 1 brana. Una 2 -brana sería geométricamente una superficie, El caso p>2 puede ser algo chocante para la gente sin formación matemática, pero realmente no tiene gran misterio, una p-brana sería geométricamente lo que técnicamente se conoce cómo una variedad de dimensión p, que son objetos matemáticos que generalizan las curvas y las superficies.

Las p-branas, para un p dado, pueden a su vez ser de diferente tipos (Dp-branas. gravity p-brnas, o g branas y unos cuantos casos más, el lector interesado puede buscar en el blog una discusión más detallada de los diversos tipos) De lejos las más habituales son las Dp-branas. La d viene de Diritlech, y la p indica su dimensión. La forma más simple de entender una Dp-Brana es verla cómo una región del espacio en la que pueden terminar los extremos de una cuerda abierta. Esos extremos pueden moverse libremente por la Dp-brana, pero no pueden abandonarla. Para cuerdas cerradas curvas cerradas) la definicion de Dp-brana es algo más delicada y no daré los detalles aquí de cómo se hace.

Las Dp-branas, geometricamente, no se supone que puedan ser una superficie arbitraria. El tipo más normal de Dp-brana es una superficie plana de extensión infinita (o al menos tan grande como el espacio disponible). Esto contrasta con las cuerdas fundamentales, que se supone que tienen (normalmente) un tamaño muy inferior al del núcleo atómico, del orden de la longitud de Planck para ser más precisos. Una D1-brana, por tanto, no sería como una cuerda fundamental pues debería tener la longitud del universo (o al menos un tamaño muy grande, siendo un posible candidato para "cuerda cósmcia"). El argumento por el cuál una Dp-brana debe tener esa extensión no se explica en los libros de texto (al menos no lo e visto en los que he leido). Se supone que debe tener esa extensión por argumentos de estabilidad. Otra configuración posible (pero menos probable) para una Dp-brana es la de una superficie cerrada. Por motivos de simetria la configuracion mas plausible para una Dp-brana cerrada sería una de forma esférica (que esta vez si podria tener cualquier tamaño).

Bien, ya casi podemos pasar a analizar el artículo en cuestión, unos breves apuntes más antes de ir con él. Las warped geometries", o "warped universes" , o también "brane worlds" son modelos fenomenológicos, inspirados en teoria de cuerdas, en los que se postula que el universo observable es una 3- brana (o una pila de ellas), y mas probablemente una D3-brana (quien quiera ver más detalles puede ir al post del blog sobre el particular). En todo caso se impone en los modelos fenomenologicos de manera "ad-hoc" que la materia del modelo standard no puede salir de la brana (matematicamente se hace usando una delta de dircac, un tipo especial, y muy conocido, de distribución) y sólo la gravedad puede moverse en una dimensión extra que sin ser de un tamaño cósmico si se supone que es mucho mayor que las dimensiones compactificadas. No obstante incluso la gravedad puede moverse de una manera bastante restringida por esas dimensiones. Ha habido bastante trabajo en crear modelos de cuerdas que se ajusten con diversos grados de precisión a los fenomenológicos. En última instancia hay que hacer notar es que estos "warped universes" tienen muchas predicciones, algunas de las cuales podrian ser observables. Qizás la más famosa sea la posible produccion de agujeros negros (o de gusano, cómo mencione en un post reciente) en el LHC. Pero con todo no ofrecen una explicacioin de cómo se habría llegado a esa configuracion. Aparentemente ese es el tipo de cuestiones que pretenden elucidarse en este paper.

El paper empieza analizando propuestas anteriores sobre el particular. Desde unas basadas en propiedades del "worldsheet" de la cuerda (su superficie de universo, análogo a la línea de universo de una particula en relatividad espacial) orginarias de Curren Vafa a otra, que argumenta que las 3 branas son las únicas que en 10 dimensiones no se intersectan con su anti d Dp-bana oligatoriamente (Las Dp-branas son objetos cargados bajo cierto tipo de campos gauge, una anti Dp-brana tendría carga opuesta. además cómo la carga se corresponde con una orientacion de la brna una anti Dp brana estaría rotada pi grados respecto a una Dp brana). Que las branas intersecten se argumenta que puede dar lugar a un mecanismo de "unwind" (la terminologia proviene de que en su modelo simplificado se asume un universo con compactificacion toroidal, y que las brnas que se pueden desenrollar-unwind- del toro). La idea final sería que las branas terminarían desintegrándose a traves de ese mecanismo de unwind y sólo las que no interesectan, las D3-branas sobrevirian en un universo en el que inicialmente estarían presentes todos los tipos posibles de Dp-Branas. En este punto es importante señalar que el hechode hablar de Dp branas automticamente esta seleccioinado un tipo especial de teoria de cuerdas. En prticular descarta los modelos heteróticos que no admiten Dp-branas. No deja de resultar curioso pués por otro lado al nivel de reproducir las familias observadas de partículas del modelo standard las cuerdas heteroticas siguen siendo los principaes favoritos. En realidad existe una red de dualidades por los cuales se argumenta que todas las teorias de cuerdas son, en el fondo lo mismo. Uno podría cuestionarse entonce porque estudiar un modelo particular. La repuesta obvia es que aunque son encierto modo equivalentes cada teoria de cuerdas correspondería a un cierto regimen posible de comportaamientos, que son los que describe mejor. El universo estaria descrito, a efectos prácticos, por uno de esos modelos (heteroticos, type I, o type II a y b, o alguna teoria M) y las dualidades servirían para estudiarotros aspectos, nome extenderé más al respecto. Obviamente estos modelos de "naturalización" de las 4 dimensiones basados en Dp-branas seguirian sin explicr porque vivimos en ese tipo particular de teoria de cuerdasy no en uno heterotico, pero bueno, seguiría siendo un muy intersante avance, por supuesto.

Lisa y Karch arguyen que el mecanismo de unwinding tienes una serie de problemas y proponen uno diferente. Su idea parte de un modelo cosmológico estandard tipo FRW (Friedman-Robertson-Walker). Ese modelo asume un universo que contiene materia distribuida de manera homogénea e isótropa (y el mismo cumple estas condiciones). Con estos supuestos las ecuaciones tensoriales de Einstein se reducen a unas relativamente sencillas ecuaciones diferenciales. En esas ecuaciones interviene una función que representa las características de la materia., lo que se conoce como ecuación de estado (asociado al tensor energia momento de las ecuaciones de Einstein, obviamente). Bien, este modelo introduce unas ecuaciones de estado que describen un gas de Dp-Branas. Analiza las caracterísitcas de ese gas y llega a la conclusión de que serían las 3 branas las que más contribuirían en esa ecuación de estado, y que por tanto son las que regirían la evolucion del universo.

Cómo he visto que me estoy alargando demasiad y que convendria describir estos aspectos con algun detalle dejo para un segundo post el resto del analisis

La teoria de las no-partículas (unparticles)

El año pasado ha surgido una nueva moda en los mundos de la físia de altas energías, la teroia de las no-partículas. El responsable de esta teoria es Howard T. Georgi, un muy conocido y respetado teórico cuya mayor contribucioin a la física, hasta el momento, fué el modelo de unificación para las fuerzas electrodébiles y la cromodinámica cuántica (es decir, todas las conocdias menos la gravedad) en un modelo basado en el grupo SU(5) , podeis leer algunos detalles al respecto en wikipedia: http://es.wikipedia.org/wiki/Teor%C3%ADa_del_campo_unificado. Ese modelo ha sido descartado experimentalmente, sobre todo debido a la prediccion de un ritmo de desintegracion del protón mayor al observado y la existencia de cierto tipo monopolos magnéticos también inobservados. No obstante ese trabajo sirvió cómo pauta para otras teorias que siguen esquemas similares. Incluso la teoria de cuerdas, de manera mucho más rebuscada, incluye elmentos de esa aproximacion, en especial las cuerdas heteróticas asadas en el grupo E8, que en una ruptura de simetría pasría a ser E6 que esta relacionado, es equivalente a nivel de álgebras de Lie, a SO(10), que es otro grupo que cóm SU(5) serviría com candidatao para unificación.

Pero vamos a centrarnos en el tema en cuestión. Todo arranca del siguiente artículo: http://arxiv.org/abs/hep-ph/0703260

La idea de Georgi parte del hecho de que muchas teorias actuales incluyen lo que se conoce cómo teorias conformes de campos (CFT de sus siglas en inglés). Georgi se plantea hasta que punto el hecho de que si realmente existieran sectores con esa invarianza conforme podría obtenerse una evidencia experimental en experimentos a las energías típicas del LHC, y, posiblemente, en otros escenarios, cómo por ejemplo la materia oscura. Antes de exponer la teoria de Georgi comentaré un poco sobre teorias conformes.

Una teoria conforme sería, hablando rudamente, que fuera invariante bajo transformaciones conformes. El concepto de transformacion conforme, en su version mas sencilla, es posible que le suene a todo aquel que haya seguido un curso elemental de teoria de funciones de una variable compleja. Por mor de que me pueda seguir el mayor número de gente posible simplemente comentar que una funcion de una variable compleja es f(z): C-->C, es decir, una función cuyo argumento es un número complejo y que, además, toma valores complejos. Una tal función puede también verse cómo una transformación de una región del plano complejo en otra region del plano complejo. EStamos interesados en un tipo especial de transformaciones, aquellas que preservan la métrica compleja salvo un factor. Más adelante pondré una expresión más general, pero de momento, y en el plano complejo, esto significa que estamos ante transformaciones que preservan los ángulos. Otra forma de caracterizarlas es cóm aquellas que transforman cuadrados en cuadrados. Por ejemplo:



Se tranforma en:



bajo un cierto tipo de tranforamcion coforme, conocida como transforamcion de Möebius, que viene dada por

1.

Bien, esta tranfomracion conforme, dada por la tranformación (que se corresponde, claro esta, con una fucnión) de Móebius es un caso particular de transformación conforme en el plano. Se puede demostrar que, en general, las transformaciones conformes en este plano complejo vienen dadas por funciones holomorfas, es decir aquelas que satiscaen las condiciones de Cauchy Rieman, que asumo conoce cualquiera que haya estudiado variable compleja. En casos mas genrales, variedades riemanianas de n dimensiones (o cosas cómo el superespacio), una transformación conforme se caracterizaría en términos de la métrica cóm aquella que cumple:

2.

Eso respecto a la gemetría de las transformaciones conformes. Podeis leer más sobre ello en wikipedia, por ejemplo en :

http://en.wikipedia.org/wiki/Conformal_geometry

o en:

http://en.wikipedia.org/wiki/Conformal_symmetry

Pero lo que nos intersa ahora es física que sea invariante bajo transformaciones conformes, podeis leer algo en wikipedia (http://en.wikipedia.org/wiki/Conformal_field_theory ) pero creo que es interesante que me exitenda un poquito más. Es posible que el caso más conocido, y el mas simple, de teorias físicas relacionadas con teorias conformes sea el campo de velocidades de un fluido bidimensional ideal. Se puede demostrar que el campo de velocidades de un fluido bidimensional, caracterizado por un vector de dos dimensiones, dependiente de las coordenadas x,y, denotado u(x,y) viene dado por un potencial bidimensional a través de la ecuacion de Laplace. Sin entrar en muchos detalles la idea es que si u(x,y) representa un campo de velocidades válido para un fluido el resultado de acpicar un tranfsformacion conforme a ese campo también representa un campo de vleocidades válido. La utilidad de eso es que esulta relativamente sencilllo calcular el campo de velocidades para una figura geométrica muy sencilla, un círculo (que correspondería a la seccion transversal de un cilindro). Ese campo representaria el cmapo de velocidades del fluido alrededor de un cilindro infinto. Ciertamente eso no es la cosa mas interesante del mundo en casos prácitos. Lo bueno de las tranformaciones conformes es que podemos encontrar algunas que transforman el círuclo en algo que se parezca a una seccion transversal del ala de un avión. Y entonces como sabemos el campo de velocidades alrededor de un fluido sabremos el campo de velocidades alrededor del ala. Por desgracia hay un "pequeño" problema. Resulta que los fluidos reales tiene viscosidad, y el resultado de los fluidos reales, no viscosos, no nos da toda la informacion. en particular no nos informa de lo que ocurre justo en las inmediaciones del ala. Los fluidos viscosos (en particular líquidos, pero en buena parte también los gases) tiene la propiedad de que "se pegan" a las superficies sólidas, es decir, que la velocidad del fluido en contacto con un sólido, en este caso el ala, es 0. Evidentemente un avion moviéndose a gran velocidad relativa no puede cumplir esta propiedad para todos los puntos del fluido. Existe el fenómeno de capa limite que cnsiste en que hay una fina capa en torno al objeto sólido en la que se da casi toda la variacion entre el valor 0 y el valor "en el infinito", osea, suficnetemente alejado. Bien, la toeria del fluido ideal informa bastante bien del campo de velocidade sfuera de la capa límite.

Puede parecer extraño que me haya alrgado tanto hablando de fluidos en un post sobre física de partículas, pero el caso es que me viene bien para explicar otro aspecto intuitivo delas toerias conformes, la invairanza de escala.

Si nos fimjos en la ec 2 veremso que le caso más simple de transformacion conforme es aquel en que simplemente se multiplica la métrica por una constante. Esto viene a significar que se aumenta (o disminuye) el tamaño del sistema en una proporcion que es igula en todos los puntos del mismo. En términos no matemáticos puede pensarse en un avión y su maqueta. La maqueta es una version a escala reducida del avión (o viceversa). Los fluidos ideales, bidimensinales, son invariantes conformes. Eso significa que la física es la misma para el avion y su maqueta. Sin embargo si tomamos en cuenta todos los aspectos del flujo de un fluido nno ideal (viscoso) y tridimensinal rsulta que la física subyacente no es invariante bajo cambios de escala. Esto significa que las propiedades del flujo del aire alrededor de un avión y las del flujo del aire alrededor de su maqueta no son iguales. Com oconsecuencia de ello en estudios experimentales hay que hacer enormes túneles de viento dónde meter alas de gran tamaño y no basta con un pequeño tunel de viento dónde poner una peuqeña maqueta.

Esto en cuanto a fisica clásica. En física cuántica, teorias cuánticas de campos y similares, tenemos que las partículas observadas, el modelo standard, viene descritas por ecuaciones que no son invariantes bajo cambios de escala, y en gerneral bajo transforamciones conformes. Sin embargo hay teorias de interés que si lo son. El caso más famoso e importante son las teorias de cuedas. Una cuerda (osea, una curva) moviéndose gnera una superficie. normalmente esa superficie viene descrita por una métrica Lorentziana, pero puede hacerse una rotacion a tiempo imaginario (el tiempo viene de que la superficie es una curva que evoluciona en el tiempo) y dársele una métrica euclidea (riemaniana). Se puede considerar que la evolución en el tiempo de una cuerda sería una superfiicie de Riemman, es decir, una genralización del plano complejo a superfices bidimensinales cuvas . Las cordenadas de la cuerda pueden verse como campos en la superficie de Riemman que engendra la cuerda al moverse (conocida como el worldsheet de la cuerda). El lagrangiano de esos campos, el lagrangiano de la cuerda, es una teoria invariante bajo transformacioens conformes. Es importante fijarse que esta es una invarianza en 2 dimensiones. La cuerda vive en n dimensiones, (hay, por tanto n-1 coordenas, i.e. campos conformes) dpendiendo del tipo de cuerda, La cuerda bosonica vive en 26 y otros tipos de cuerdas, las supercuerdas, viven en 10. En todo caso ninguna de estas teorias es, directametne, una teoria en 4 dimensiones, como la que describe el modelo standard. Hay otro tipo de teorias que si viven en 4 dimensiones y que son invariantes conformes. Estas son teorias maximalmente supersimétricas. Esto siginifca, para 4 dimensiones, teorias con 4 cargas supersimétricas. Estas son el tio de teorias que entran en la conjetura del Maldacena, o conjeutra AdS/CFT, que es uno de los ´tópicos más estudiados en supercuerdas durante los últimos años.

Comentar que aparte de en física fundamental las teorias conformes juegan un papel primordial en el estudio de los cambios de fase. Un cambio de un estado de la materia a otro, por ejemplo de sólido a líquido, o de líquido a gas. Las cntidades intereantes en el estudio de esas transiciones de fase (tipicamente funciones de correlacion) puede verse que en el entorno del cambio de fase poseen también invarianza conforme. Dicho de otro modo, en un cambio de fase estan interactuando fenomenos físicos de diferentes escals en condiciones de igualdad. En fi´n, no me extenderé en este aspectos. Los he mencionado para que quede claro que estas teorias conformes sonútiles en otros campos de interés eminentemente práctico y no sólo en física de altas energías (que no es uqe no sea de interés práctico amedio y largo plazo, claro).

Hasta aquí los poloegómenos. Queda claro que es interesante preocuparse por teorias conformes. Ahora bien ¿cómo hacerlo?. Un aspecto que no he señalado hasta ahora es que las toerias conformes estan relaconadas, en fisica de particulas, con partículas sin masa.

En general no se puede acoplar una particula del modelo standard, con masa (el modelo standard no es invariante conforme) a una teoria conforme. Normalmente lo que uno se había planteado es que la invarianza conforme quedaba rota en algún punto, dango lugar a ciertos tipos de partículas y uno se preocupaba de que esas particulas fueran el modelo standard (o algunas generalizaciones). Georgi va mas allá y se plantea la posibilidad d que , a escalas de energía mayores a las observadas, las partículas del modelo stnadard interaccionen con campos conformes. Lo interesante es que si hay una interaccion directa entre el modelo standard y las pas particulas sin masa de una teoria conforme el resultado no dará nunca una partícula correspondiente al modelo conforme que pueda ser observada (de ahi el nombre de unparticles). Pero cómo resultado de esa interaccion la particula del modelo standard habrá cedido energía y momento a algo no oservable. Lo que si sería observable es la pérdida.

En el artícululo mete un término de interaccion entre campos del modelo standard y campos conformes. Esta es una interaccion no renormalizable que se supne qu ecorresponde a un modelo efectivo (útil sólo en ciertas escalas de energía, pero que no se supone que sirva para explicar la física a cualqueir escala de enrgía). Obtiene una factorizacion de las secciones eficaces (que nos indican cuanta energía "se pierde") generales. Luego particulariza a algunos casos, y en concreto a uno con quarks y gluones. La idea es que los resultados dan pérdidas que podrian ser observables en el HC. Posteriores desarrollos vinculan esta teoria de las unparticles a la materia oscura.

Claramente no hay evidencia experimental de esta teoria, pero lo bueno es que si fuese cierta podria haberla, y en breve. No es una teoria fundamental pués sería una teoria efectiva de algunos aspectos de otras teorias. Con todo e una buena idea y se ha convertido en el artículo más citado en fisica de altas energias del año 2007, osease, el tópico en el que mas se esta publicando. Con todo, al no ser una teoria fundamental, no resuelve los grandes problemas de la fisica teoria actual, en particular no aporta anda a la gravitacion cuántica. Pero no deja de ser intereasante.

Should cosmology be important for fundamental physic?

I have, at last, readed the following article of Leonard Suskind on the antropic landscape:

http://arXiv.org/hep-th/0302219 v1

Before briefly discusing it I will mention that I have also beeing reading the chpater on cosmology of dinés book "supersymmetry and string theory" and some stuff on blogs and forums about cosmology. I must say first that a few years ago (maybe a decade) the view of cosmology among theoretical physics (or at least the ones I speaked too) was diferent that what actually is. The viewpoint was that there were physic firmely based on carefull and exaustives experiments made in earth, which were the core of physics and that as an interesting toy you could try to aply that laws to the universe as a whole and to see how well it fitted. The consensous was that the important aspect was that the universe could be coarse grained described by a, relatively, very simple models. If there was some particular deviation it was a good thing to try to improve the models to fit it, but it was not a preferent problem.

A good reason for not taking too seriously cosmology is that the universe as a whole is a very bad experiment. There are too many possible variables (some of them probably ignored) playing in complicated manners. In an earth based experiment you can modify the settings so that only a few parameters are relevant for the quantity you try to messure, but you can´t do something similar with the whole universe.

But from a time to now the viewpoint has drastically changed. The string theory comunity have the viewpoint that it is very unlikely to see quantum gravity effects in colliders (an exception could arise if brane universe scenaries are correct) and, in general, another stringy effects are also hard to see. On the countrary the early universe, with it´s high energy, would be the place to search for this efffects. I must´say that I have become surprised when I have seen some of the effort made in this line of research. To say one I never even had thoguht that someone could have cared about the possibility that the decayof a gravitino, the supertpartner of the graviton, could be dominant at the same time that baryogénesis and that it could rsult in breaking of light elements. Or that a similar situtation could exist fo rmoduli fields of supersymmetry or string theory. There are workarounds for this posibilities, of course, but, what the hell? Who cares?. I mean, the interest is to find signs of supersymmetry now, not in some scenaries that could have existed, but that are excluded by observation.

But, ok, If some people wants to work in that things is fine for me. Even better is that people could be using string theory to calculate potentials for inflaton fields when they previously introduced that potentials by hand to try to fit observaations. The LQG comunity are using extensively the canonical (hamiltonian) aproach to do a lot of toy models. Irrespectively of how good or bad you thnk about LQG their effort is coherent in their internal logic.

In general I don´t dislike when people are triying to use fundamental physics (or should be physics,i.e. non still proved theories like strings and LQG) to see how they can help to fit cosmological observations. My problem is when the flow is in the reverse direction, when people try to modify physics (or should be physic) froms cosmological observations. A previous aclaration is necessary. If some theory predicts an aboundancy of phenomena such as monopolesor cosmic strings and hthat boundance is not observed one, certainlly, need tobe cauptios with that particular model. That is, one could be aware that the model can´t be the final answer to unification physics (althought still could be that some factor is the cause of the nonobserved aboundances and the model still be valid). But one would not rule out a model, with physical consecuences of it observed in earth, because of cosmological situations. Nor one would leave the traditional way to do physic because or cosmological observations.

Well, as everybody who knows the actual state of string theory knows this is not the case. The observation of an small positive cosmological constant has hanged the way to do physic (or at least string theory). The problem with that cosmologial constant is that string theory, as well as any quantum field theory for what matters, has a problem to explain it. If one calculates for an ordinary QFT the vacuun energy one finds that it is aan few orders of magnitude higher than the observed cosmological constant. If one has a supersymmetric theory, with unbroken supersymmetry, bosonic and fermionic modes canell out and one can get a 0 cosmological constant. The "little" problem with it is that suposedly supersymmetry is broken.

Well, the problem has existed from a long time, would it be with 0 or with a tiny cosmological constant. And people has lived with the problem and has been happy doing physics. But now it results that string theorists had a good confidence that afther all string theory could fit well with a 0 cosmological constant. And when the have found that it could be non zero (the experimental status of this is good, with at least 3 partially unrelated phenomenae indicating it, but still there are possibilities that afther all it is 0) the have become nervous and have modified the way to thnk about string theory, and it´s vacuums, to accommodate the reslt. In fact they have beein inspired by a model made by Weinberg a few decades ago. A model who was nothing but a curiosity who none cared too much because the had more interesting things to study.

But now you must leave with the idea that the universe must be in a sperposition fo supersymmetric vacuums, with 0 CC, and nonsupersymmetric ones, with a big CC, so the promedium is the observed one. Even you must face the possibility that this low value is hold only in a, relatively small, part of the universe separated by horizonts from anothers. And the criteria (while someone finds something better) to make physics in this superposition of vacua is to use anthropic principles.

Well, nowadays even renuent people such like Lubos Motl, seems to accept this status. My viewpoint is that there are a lot of things to do in string theory (or out of it) which is mainly unafectd by this change of paradigma. So, beyond being to the expectative that somone finds a better solution to the CC problem, I wouldn´t care too much about that landscape and would worry about other things, at least if that is possible (and I guess it will be).

The phenomenology, the abstract theory and the weird speculation

I am almost sure that if some high end professional of string theory hs readed the previous entry vill have renewed his very bad thoughts about the physics blogosphere. If, instead, he would have readed the post about Horava-Witten theory and brane univereses I guess taht he instead will have felt more confortable. This is because the post of topology vs group theory was speculative, probably too speculative (althought not necesarily a nonsense I hope), while the one in brane universes was very conventional and not controversial at all. In fact I could have made something similar and I could have limited myself to enumarate some of the many, many well stablished aplications of topology to physics, explaingn briefly the details and by signaling it´s numerical and conceptual superiority over the group theory aplications and I would have a "safe" post. In fact I´ll probably do some of this in posterior entries, but that wouldn´t show the viewpoint I wanted to transmite.

Afther this I am going to explain the reason of the topic. In physics, even in theoretical physics, there are many levels. One one side there are the "old fashioned" particle physicis. You can find some of them, teachers with academic positions in good universities, which hate even the yang mills theory as explained, for example, in the Cheng and Li book of particle physics, (or in any conventional QFT text book for what matters). They prefer the very heurisitc exposition of the subject presented in books such like the one of Halzen and Martin "quarks and leptons". This people usually like "solid physics" from colliders. In an intermediate, most reasonable, state are phenomenological people who accept and like QFT. This people can be working on hadron physiscs or even dealing with some posible phenomenology related to supersymmetrtry, mainly the MSSM (minimally supersimmetric standard model) and supersymmetric unification. Some even go beyond and are interested in string theory or (possible) alternatives to quantum gravity.

To read books for this people is a very good way to learn actually stablished physics and possible near future physics. I know two great books of this characteristics. The excelent one of Martin, squires and Collins "particle physics and cosmology", and the very recent one of Michel Dine "Supersymmetry and String theory". In some sense the last one is an (unintended) update of the previous. To be honest I find more understable and better writen the one Martin et all that the book of Dine. But still is a good book. The introduction to supersimmetry is very diferent, and the book of Amrtin et all includes also supergravity. On the other since the Dine´s books goes a lot deeper into string theory, withouth beeing a rigurous book on pure string theory (of course because that was not i´s purpose). I guess that everyone should read some book of this characteristics from time to time to keep contact with the details of phenomenology.

But detailled phenomenology is not everything in theoretical physics. You need to give good foundation to the enviroment in which the pheonomnological calculations are done. This requires at least to understand the proper foundations of quantum field theory and supersymmetry. A good modern exposition wuld be the three volumes book of Weinberg, but honestly, I see that book more like a reference book that anything else. A poit that string theorist signal is that one should be sure to study modern renormalization theory (It is not the same as the renormalization theory in classic QFT books such like the Itzikson-Zuber). I am doing this just now. I did a bad coice of review article that has delayed me for a time, but I guess that I am beguining to gain proper understanding of it. Beyond QFT there is supersymmetry. The books I mentioned previously are "all purpposed books" but there are textbooks specialized in supergravity. I have ocassionaly readed one (but unfortunately it is not in a very asscessible place now so I cant give you the exact reference). They concentrate in more theoretical aspects of supersymmetry and while string theory is a much more promising area of study they still have their point.

And of course we have string theory, and all the possible alternatives. That are pure theory. In fact still instring theory there are more "phenomenological" aspects, for example to find realistics compactifications or to solve the cosmological prblem, and more "theoretical aspects". Of this last I could signal to try to understand better what M-theory is, the superstring field theories, and the Maldacena conjecture, to say ones. Other topics, for example black hole theory, are somewhat in the middle.

And now the last topic, the "weird speculation". This is a broad subject. It can go from simple tings, like to get a proper understanding of the theories to more risked things. I´ll give a few examples of the first point. A very basic one is from nonrelativistic quantum mechanics, collision theory. When I was teached it I understood everything perfectly untill we arrived to resonances. Them the teacher explained you that the imaginary poles of the S-Matrix where resonances. Fine, it was a relatively easy thing to find that poles and to work with them. Inmediately later he toldd you that heuristically you would interprete that resonances as "metastable states". But he didn´t explain why. The book that he followed, and a fe other I readed, didn´t say more. Of course for me this was totally unsatisfactory. I could pass the exam withouth mayor problem even doing an exercise about resonances. But from my viewpoint I didn´t understand resonances at all. I asked the quesetion from time to time, but it was not untill that I casually readed the Landau chapter in the subject. There they explained why this math prescription came. You neded to think in outgoing waves with imaginary exponent and how this was related to the metastability (read the book for the details if you don´t know them, It is a total "you must").

In QFT I havent´t found (or at least I don´t remmeber them now) similar situations. But in strign theory I have found many. To beguin the very basic idea of string theory, such as I explained in the first entries of this blog. To read all the modern boooks on the subject didn´t convince me a bit that the idea of an string, such as presented, is a convincing one. Like string theoriest don´t care too much about it I try to do "weird speculation" about the subject. My initial idea of knotted strings is easy to state in a formal way. Afther reading the chapter 13 (if Idon´t remmember bad) of the Green -Schwartz-Witten bookd I have gained the knowledge that open strings can join their endpoints and to form a closed string. Well, aparently two open strings could get closed interlinking one to another. You would describe the collective state by a hilbert product state of the separate strings. If this configuration would be stable you would have states that would look like mixed states of conventinal particles. To elucidate aobut if this stability could exist I must go to another theory. Rañeda and Trueba made a topological formulation of electromagnetism. This consisted of expresing the vacuum Maxwell equations in terms of different fields. This allowed them to clasify the solutions with bounded energy (i.e. vanishing in the infinity) into topological sectors with different of a topological quantity which could be identified with the heilicity of the electromagnetic field. The configurations with non trivial topology (identificalbe, among another possible ways, as a kind of knoting) presented extra stability, and it was conjetures that they could be related to the atsosferic pehnomenon know as "ray balls" (the actual article is published in nature, so be totally sure it is not "crackpot phuysic"). The idea could possibly be extended to Yang Mills theories. ANd here is where I think that it could be connected somehow to this "knotted strings" . If the string which get knotted are in a vibrational state corresponding to yang mill fields it could be that they could be somehow resemble some knotted configuration of Yang Mill fields and become stable. Of course this is very wild speculation, and withouth confronting more detaills and consistency checks is not something to be considered seriously.

The key point of knotted strigs is that if one takes serioulsy the idea of string theory they I.M.H.O. would be considered (soon I´ll explain another possible argument). But I still am dissapointed with the idea of strings. I am triying to search for a natural way inwhich strigns make sense (and don´t disgregate intoit´s constituent points). I knowt thaat one should addopt the coherence of the string as a postulate. But I still try to go beyond that. From the accepted string theoretical viewpoit there are a few possible aproachs to it that I try to consider. S-duality relate the strong coupling limit of an string theory to the weak coupling limt of another. Under this duality fundamental strings of a theory canbe identified with D1-branes of the other. But D1-Branes suposedly can be charasterized as some kind of topological deffects. Topological deffects are stable things, so that could justify a posteriory the stability of fundamental strings. The problem is that to arrive to the D-brane idea one must beguin with perturbative strings. There is the viewpoint of "D-brane democracy". This means that dpednidn on energy,or maybe better said, inthe history of the universsee, of thepossible equivalent ways to describe string theoyr (all the five strig theorys, M-theory and F-theory) the universe is in an state in chich "fundamental" strings are agood description of observable physic, but still the reason of their stability must be explained in the D1-Brane ansatz.

A more drastic departure to try to assign a "naturality" to the idea of string (here is where the profesional string theorisst will definitively lose it´s patience if he has resisted untill this pint) could come from the following scenary. In some aspects thje idea of string separates the universe intotow scales. The scale greater than the string and the scale smaller (In fact d-branes canprobe distances smaller than the size of an string, but let´s accept the premise for a while). Well, let´s try to get the same idea in a diferent viewpoint. We must have an "inner theory" for distances smaller than the planck scale that in the limits reproduce ordinary quantum field theory. Under the planck size the usuall notions of QFT and relativity (in particular the Lorentz invariance) would dissapear, or more properly said, they could not experimentally stablished. That would mean that if we try to be sure that if a particular state is an electron, a photon or whatever in distances shorter than the panck one we cant so we must deal with states that are a superpostion of all the possibilities. String are good for it. Of course this is not more than cheap philosophy in this state. Another way totry to sse this I gues that it can be related to M-theory. While reading about horava-witten theory I have got more involved withthe bizarre aspects of M-theory. FOr example there are arguments that it´s proper description cant be given in termos of a lagrangian. This means that it doesnt go under the prescription of a variational principle. There are not classical configurations that minimize and action and quantum corrections. But this means that we are in a democracy where every trajectory is equally good, and there is not quantum physic. On the other hand M-Theory is the strong coupling constant of string theory. I am not totally sure but i think than that means that it studies the behaviour of the shortes vibrational modes of the string. This modes somehow would explore a region where evrything is beyond the planck scale. AS the planck constant has magnitudes of action whe are exploringn zones wher the notion of action does´nt apply. This could explain why there is no lagrangian (i.e. action based) description of M-theory. Once agian, this is weird, and weak, and cheap speculation. Dont confuse it with anything accepted by the mainstream os string theorists.

Another thing in string theory which I want to understand properly is why D-branes are suposed to be infinitely extended. If a D1-brane is the dual oof a fundamental string, a very shor object, why the hel it must be infinitellly extended .Somone pointed me that infact a priory it wouldn´t be necesary, but that stabiilty reasons force one to have infinitely extendend D-branes. Well, I don´t know where that calculations are done, may be inthe K-theory program, in the analisys ob non BPS branes, it could be related to th tachyonic condnesation, or maybe it is explained in some arkane text about the M-branes. At least now I have the certainty that it is not a trivial thing and that the a priory idea that D-branes would be of a finite size was a reasonable question. B.T.W., I had said that tere were another possible way to explain ths stability of "knotted stirngs" if that configuartios would form. Of course that would be seen to come from a D1-Brane perspective. If infinite sized branes cross among them it looks like that would be very stable topologicaly.

This was weird speculation within string theory. Now I am going to say an example of speculation outside it. Pitkannen proposes in it´s topological geometrodynamic that oneshould worry about the possibiilty that because of some reasonone would care about p-adic metrics. In a p-adic metric ponts very far away inthe conventional metric are very nearby. I think that he try to present an scenary where the nature of the real world is p-adic (at least in some cases). That would explain, inhis viewpoint the colapse of the wavefunction. He subscribes a viewpoint where concsciece is related to that, and it implies that humans brians have the capability to ifluence long distances. Well, maybe he would like becuase of this some weird paper (commented inLubos blog) that hte observation of the cosmological constant has modifeid the stae of the universe, or maybe not, you can ask him in his own blog. What I wondered yesterday was nothing of this. I had said that if one tries togive a ynnamical topology change, explianing the formation of a wormhole, it appear natural to expect that it connects nearby distnces. Infact quantum fluctuation (basically here the usual Heisenberg uncertainty betwen postion and momenta)could justify an small posibity that it would connect far points. But, if in some range the nature is actually best described by p-adic (or adelic) metrics (afther all there are people worriying about p-adic strings) then it would be natural that wormholes afther ll would connect points that in the ordinary metric are far away.

Well, I hope that if I am very clear staitng when I speak about accepted physics and when i am divagating (and triying to pose a quote to the degree of divagation) the reader can actually have a realistic perspective of physics, and maybe somes even fun (interesting would be a too exigent word) fan the weird speculations. Anyway, I´ll try to post mainly about divulgation of conventionally accepted physics.

Topology vs group theory in physics

I have said in some ocations that I dont´t like too much group theory, and that I prefer to study topology. I am going to try to explain a litle bit about it.

One of them is pureley mathemathical, I prefer to study things like homology, cohomology, sheaves, spectral sequences, cobordism, morse theory, K-theory and mostly all the topology in the world than group theory. Group theory, and it´s representations, is more or less always the same, but there are a lot of diferent topological tools, all of them with their own peculiarities.

But maths is not a reason a physician could accept. Well, let´s go to physical motivations. One of the goodnes of topology is to try to decide what interestign things happen when one goes from the local tothe global. For example infixing a gauge for a gauge theory you have that any gauge fixing is local and that you can´t extend it to the whole of the phase space. One consecuence of it is the so called Gribov ambiguity. In fact there is a problem with this. Most topological theories are intended to study finite dimensional manifolds and the phase space of a gauge theory is not one of them, so the path is not straighforward from the topology books to their applications in this problems. For example, the BRST operator of gauge theories certainly has the same characteristics than the external derivative of diferential forms. You can form the de-Rham cohomology with the external derivative, to prove that it is equivalent to another cohomologies and use it as a calculational tool for finite manifolds. BRST is usefull, certainly, to select physical states, but I don´t see in the literature that it would be applied to analize the topology of the infinite dimensional phase space. Fortunately there are other things where topology, in its more straightforward form, is interesting, relativity.

One of the things that I find more interesting in general relativity is the role of topology change. The Einstein equations fix the metric of space-time, but don´t say anything specific about it´s topology. In most conventional problems the topology is somewhat assumed. For example in ths schwarschild solution you are studiying something which is topologicallly R³, or, if there is a black-hole you could doubt about the nature of the singularity and to deciede to excise it. Schwarschild space tie is static so it is not problematic. But wen you have a non static space-time things are more intringuing. At a given "time" you have an hypersurface (the technical key word is "slicing"). The natural questions is to wonder if time evolutions, given from the Einstein equations, could change the topology of that hypersurfaces from one time to another. That is a very mathemathically interesting problem in classical gravity and it is usually studied using cobordisms betwen the hypersurfaces. Cobordism intuitive idea is very easy to understand, you wonder when two given n-manifolds can be the border of another n+1-manifold. If you don´t whant to learn cobordism you simply can go to the results which states the criteria under a objects more best known to physicans, characterisitic classes. The results are that if you don´t impose aditional conditions you actually can have topology changes. But when you impose things such like causality and similars the things are more obscure and probably topology change is forbiden. I must say that even if you understand the detaills of the math involved it is somewhat surprising to try to thnk into the details. Afther all in one point you have a metric for a manifold, and later a metric fo ra diferent manifold. And somewhere in the midle you must have a metric which would be good for limit cases of that manifolds. Try to imagine a two dimensinal cae. For example the traditional idea of the formation of a whormhole. You beguin with a 2 sphere and you go nearing two points of it (think for simplicity of two opposite antipodal, points. In the limit beofore the change to the new topology you would have an sphere with the two antipodal points idetntifieds. Afther that you would have a torus.

Try to think about what´s going on just in the intermediate betwen the two cases. Inmediately before you have two tangent spaces which in the intermediate point must be identified. How to interpretate that physically? For that urpose I guess that topology is not the better tool and that the answer would rely in algebraic geometry. I am actually triying to learn algebraic geometry (beyond the one exposed in string theory books) so I can´t go further into this.

I have said "whormhole". Certainlly there is a lot of literature about them. But what I have readed doesn´t actually says too much about the topology change. For transversabble (minkowskian) wormholes you simple decide based in natural requirements a guess form for the metric. But it is all static, you describe the formed wormhole, not the process of it formation. Some tiem ago wormholes where considered funny curiosities usefull for science fiction tales. With the observation of the acclerated universe the thing has changed. The reason is that the existence of a cosmological constant, or of phanthom energy (another possible cause of the acelerating universe) give to wormholes a different position in physicis. The reason is that transversable womhholes require the existence of energy violating the weak energy condition. Usually it was thought that alghoutght it was possible to have small amounts of this matter (by means of quantum effects such like the cassimir effect) it was very unlikely to have too much of it. But the acclerated expansion of the universe make svery plausible that this matter exists. For example in the branworld universes you can have five dimensional matter which in five dimesnions doesn´t vilate that condtion but that it seems to do so in four. The main conclusion is that because of many possible realizations womrholes in a acceraated should exist, and that one must try to find a reason to explain why the don´t exist, or, better, to try to search for them. This could be possible, for example, triying to detect "macroscopic monopoles". The reason is that an usula magnetic field in the vecinity of a wormhole could appear as a magnetic monopole for some observers. Semengly there are concrete proposals for searching them, but I am not totally sure about how the are evolving.

By the way, note that I have said that wormholes are being heavilly studied in the braneworld scenaries. This is one of the reasons I have studied more in deep the Horava-Witten models. I didn´t feel confortable by only understandin the phenomemological approach. In the near future I´ll go back to the study of wormholes, both in conventinoal and in braneworld univeres, and not only to it´s static aspects but to try to understand the dynamics of the formation. If you are a fan of science fiction I can give you a reason why the could be interestings. In SF histories they are usually a tool for interestelar travel or a time machine. But if you think about it if you actually tri to construc a wormhole the most probable thing is that you would connect points that are (very) near one of them. Later you could try to separate the throats of the wormhole. They would be usefull as a fast interstellar travel device only afther you carry the throaths that distance by a conventional way (suposing that the inner distance bethwen the throats doesnt grow). But there is a possible, more realistic, and more usfull way to use a wormhole. You could put one throat near the sun surface and the other near the earth. The solar energy going inside the womrhole will not spread so you will send to the earth the same energy of the sun as the area of the throats. A crude estimation shows that a throat of a few metter of radius will send to the earth the energy that the human the whole race needs. Of course you need to use an intermediate energy vector to use that electromagnetic energy, but that are "minor detaills" xD.

Still one could think that wormholes, or topology change in general relativiey is a too restricitive field. I don´t think so. In string theory there is a great problem. Triying to seek a viable compactification (or going into the landscape if you like that things). But if one thinks a bit about it a compactification is ultimatelly a topology change in the underliying space. Almost all of the work is being done to try to seek for good compactifications. You use a lot of topology and algebraic geometry for that. That is because you study the topology of the resulting space, but you dont wonder how you arrive to that compactificated spaces. String theory goes beyond general relativity, but still it could be interesting to see what a general relativity (or something near to it) could say about that transitions. For example, what kind of matter would inforce that compactifications?

Until nw I have mainly mentioned topology, what about group theory? I am not going to alk too much about it, but, instead, I´ll try to relate it somewhat to compactifications. The easiest place where group theory can appear in quantum physics is in the theory of the angular momentum of a nonreltivistic particle. Rotations in space are described by the SO(3) group. Th universal covering group of SO(3) is SU(2). On the other hand when you have a quantum system with rotational invariane it can be said that, just like in the classical counterpart, the angular momentum is conserved. The classical angular momentum is L=rxp. If you go from the classical momentum p to the quantum operator p you have the definition for the quantum angular momentum. Youcan show that their component´s don´t conmute so you can only observe one of them simultaneously. On the other hand the squared angular momentum L² conmutes with all the components so you can observe it. You can connec the physics with the group theory saying that L² is a cassimir operator for a representation, and that you can relate L+- = Lx +- iLy which act as ladder operators, similar to the a+ a- of the harmonic oscilators, to elements of the group theory of SU(2).

This was an external symmetry. Latter, with the advance of particle physics and QFT appeared internal symmetries, and they were related to easy groups. SU(2), SU(3) and U(1). And the first unification attemp was SU(5). The same technicques used for the group theoyr tratement and a few others allowed to do a lot of calculatiions in particle physicis. Another point of group theory was the role played by the poincaré an dLorent group to the classifications of particles. One could relate the spin of a particle to a representations of the Lorentz group. Of course all of this is well known by a lot of the people that wouldmost likely wuld be interested in reading this blog, so which is my point against group theory.

I said that I wuld relate group theory and compactification. Afther all one of the points of stirn gtheory is to recover the ideas of Kaluza-klein. One can show (I did a post, in spanish, in this blog about it) that an five dimensional space compactified in a circle makes that the "external" gravitational of the five dimension becomes an U(1) "internal" simmetyr equivalent to electromagnetism. This is the ideal case. But nature is not allways ideal. In facto it usually isn´t. The hidrogen atom is almost perfectly shperically symmetric, but because of electron, electron-interaction other atoms are not. Still angular momentum is a very usefull quantity, but it doesntt any more is related to a perfect "reall" symmetry.

What about the circle of the compactification?. On could expect that it would be a perfect circle. Afther all symmetric configurations are commonly the right solutions for optimization problems. But if we think in the possible dynamic of the compactification one realize that that circle still i space-time, and because of general relativity space time is dynamic. So one could expect that it will not be an static perfec circle but that it will be subject to fluctuations. But if the guge symmetry really is a reflection of the diffeomorphism invariance of the compactified space and this is subject to fluctuations it can´t be a perfect symmetry. Moreover, group theory is good to describe the state of th symmetry in a given moment. But there is symmetry breaking,and group theory is not good to stdy it´s dynamic. In fact the dynamic of symmetry breaking should be equivalent to the dynamcic of compatification. In fact there are "dictionaries" translating symmetry breaking into D-brane theory language. And there are also ways to see gauge symmetries in terms of branes which go beyond the idea that I explained here. But still I think that the idea aapply. Group theory is ufull to analyze statics. But any internal group theory should be related to a compactifications, and you can use topology to study compactification. And topology is mathematically richer than group theory, so it can let you go further. And the key ingredient of analizying compactifications, or symmetri breakings could be related (or one could nspire in the study of) to the dymanic of topology change in general relativity, and indirectly to whormholes. In fact rolled dimesnions have an asociated casimir effect. Maybe this could be an alternative explanation of the cosmoogical constant, but I don´t see exactly how. By the way, the cassimir effect is anothe rthing topological in characters, as well as the arahano-bhor. And solitons and instantons in gauge theories can be studied by means of topology. Definitivelly I think topology is mre interesting that group theory. And possibly algebraic geometry is necesary to complement topology in some cases.

Afther this post I hope that you will understand why I don´t thnk that Garret-Liisi theoyr could be related to important and deep questions in physics. But of course that is only a tangential point of the post. Ah, the most veterans readers of this blog may answer about "knotted strings". I stil don´t see a clear reason why they couldn´t exist, but I still lack a full understanding of many aspects ofstring theory. Obviously is not the easist thing in the wolrd to understand, but it is interesting, certanly.

Exceptionally an entry about Garrett Lisi´s ToE

I was aware of the existence of this theory since the post of Lisi in the Sabbines Hosfander "inspirational series". There he stated that "he was cooking a theory to kick the string theory ass" (or something quite similar). Not too surprisingly in the comments sectionhe was quilified by Lubos Motl as an crank.

I am not a terrible fan of group theory and this proposal of ToE (theory of everything) relies heavilly on it. Worst, it depends on E(8). Almost all my knowledge of E(8) comes from the appendix to chapter 6 of Green-Schwartz-Witten book on string theory and from the corresponding entry on wikipedia. More important than this is that it is hard to conceive that it could be possible to gain any insighth in quantum gravity by means of group theory. I mean, gravity is about diferentail geometry, maybe topology. At most it could be thought that gravity is about fibre theory with S0(3,1). Moreover, the Colleman-Mandella theorem states that it is impossible to join the gauge groups and the Lorentz group into a greater group. Everybody having studied supersymmetry knows this anyway (because supergravity scapes this no-go theorem). This is the first objection which Lubos made to the paper when he did his comment (you can read it here).

Garrett replied to that objection in a thread about his theory that is beeing discused at physics forums, concretely this . To be honest I didn´t follow this thread beyod the second page, but I am sure that a lot of information can be found there, as well as the correponding entries in the blos of Sabine Hossfander and Peter Woit (in spanish you could try the one in Migui's Forum.

With so many discusions going there I badly can say anything specially interesting. I find more encouraging the papers about the proof of the Maldacena correspondence (not conjecture any more) or one stating that type II A flux models (closelly related to some kind of braneworld scenaries) are not viable because of the lack of inflation.

So, why an entry about this topic afther all? The main reason is some blogs attacking Garrett Lisi´s not because his theory but because ¡he is a surfer!. Aparently the fact that he works teaching surf and snowboard is enoguth for this people to disqualify a theory. First, this is not the whole history. Lisi is financied by some organization named FQXI. Second, and most important, he seems to have contact with important people in the LQG community (which of course have given a warm wellcome to the theory and are wondering about intergrting it in an spin faom model). Also it is important to state that Lisis has a PhD in physics. All that is much more that Einstein had when he did his five famous contributions to physics in his "anni mirabiliies". But it is not a question of haveing "contacts". The point is that better or worst Garret has an original theory coherently presented in an standard way. Some of the ciritics of his work in the blogosfere have not some mayor contribution to physicis, and it is very unlikely that they could make something beyond very conventional and irrelevant contributions. For sure they are not going to ever make a paper which would get a tiny part of the(deserved or not) impact of lisis´s theory. If Lubos decides to say that Lisis is a crackpot he has behind him a couple of good papers in string theory, and a wonderfull blog with a lot of info in string theory (among other more questionable subjects). And he always would argue using physics (althought he can twist a bit some arguments xD). But his , imitators?, simply have not the authority to be so displicents about this questions.

Once I decided to make a post about the theory I did a quick reading of the paper. He beguins doing a brief summary about basic facts of the standard model and about lie groups theory. In that aspects it looks somehat more like a thesis article than a conventional review article. The fun of this is that it makesit accesible to a broad audiency. Afther a lot of statements relating group theory objects and particles of the standard model (and a few other which should be oberved in the future LHC is his theory is correct) he ends up with an action. The action takes the form of a BF theory, the best friend of the "spin foamers". I am surpried because I would expect gravity arising in a totally diferent way, and it makes me hard to see how unification could arise if gravity relises into this theory. But I guess that this question, and many others, would be addressed in the links that I gave about so I invite to my eventual readers to search there.

A last link, to another blogger talking about this theory. the one in U-duality. He talks about similtudes of this theory with something called homnogeneous supergravity, and possiby with topological string theory. Don't ask me why, but seems that not all string theorist are so negative about Lisi as Lubos. If I would have to give a recomendation about the paper it would be this. It seems to be an entertaining way to learn a bit about E(8), which plays an important role in some aspects of string theory.

O.K. I did this "obligatory" entry. Could you please separate that gun from my head? :P.

Update:

Jacket Distler also has finally made a post about the theory, you can read it here

I find it particularly interesting, as well as the discusion following, in which Garrett appears. Jackes identifies a weak point in the maths, and Garret agree, that if not overcomed would mean that the theory is useless, or more properly said, inconsistent, even at the classical level inwhich it is formulated. Well, as I said before, still the paper could be usefull as an introduction to E(8).

Brane world scenaries and their stringy/M-theory realizations

I bet that among the "vocabulary" of string theory the two that more broadly have expanded in the layman are "Calabi-Yau" and "warped (or brane world) universes". I have already made (in Spanish) a brie introduction to compactifications and Calabi-Yaus. Now I am going to talk about the warped universes and related questions.

I dón´t know the details of the history, but the "heuristic" aspects are clear. After the second string revolution there were two mayor new ingredients in string theory, D-Branes and M-Theory. D-Branes allows the picture of vectorial guage particles trapped in a brane while gravity (.i.e. gravitons) being able to escape the brane and exploring the extra dimensions. This wouldn´t be so important without M-theory. M-Theory lives in 11 dimensions, instead of the superstrings who live in 10 and the nature of the 11th dimensions is somewhat different to that of the 6 extra dimensions of superstrings. In particular it is reasonable to expect that it´s size could be greater than the (Calabi-Yau, or similar) compactified dimensions of the superstrings.

The "natural" scenario seems clear. The universe could be a D3-Brane with the standard model attached to it. The particles of the standard model would be related to a "Calabi-Yau" compactification of 6 of the additional dimensions to a planckanian size and we still have an aditional dimensiosn whose size is not constrained to be planckanian. How great could actually be?.

Well, in the late nineties Arkanni-Hammed, Savas Dimopulus and Dvalli analyzed the question in an a very simple and general framework. They proposed that we would live in a D3-brane and that all other dimensions could be macroscopic and only accessible to gravity. This trivially implied that to short distances Newtonian gravity should be modified so that it would have an 1/R^{2 + n} behaviour, being n the number of additional macroscopic dimensions, instead of the usual, with n=0. The implications of this new behaviour would be that at short distances gravity would be more intense. Surprisingly at that time gravity hadn´t been measured at short distances and the bounds for the distances where the extra dimensions would appear were as great as a millimetre. Soon a few experiments were realized and new bounds arrived. I am not totally sure, but nowadays the allowed size is on the order of at most a decimal of a millimetre. Also it has been discarded (or at least is very unlikely) that more than an additional dimension would be macroscopic (in the sense of non Planckanian).

This ADD scenario was certainly very naive. But the idea of an extra macroscopic deserved further attention. Two different ways to approach it appeared. A phenomenological one the Randall-Sundrum brane world models, and purely string theoretic one, the Horava-Witten theory which realised the idea of heterotic M-theory. I will begin discussing the first ones.

Lisa Randall and Cundrum Sumdrum proposed an scenario where gravity was prevented from "leaking" in the extra dimension was a curvature effect (a warped compactification). They proposed a metric of the form:

1.

Here x represent the coordinates of the usual 4 dimensions and y is the additional dimension. It is assumed that the four dimensional brane is the boundary of a bulk which is a portion of an AdS₅ geometry. (this also allow to relate the Randall-Sundrum sceneries to the AdS/CFT correspondence, which, incidentally, has been proved in a very recent, yesterday when this is being written, paper, available here). The parameter l in the metric of the previous equation would be the curvature of that AdS space.

The exponential factor of the metric is responsible of confining gravity. The reason behind the y being in modulus is that we are in an scenario with two branes. One of this correspond to the visible world, the other is a "hidden" brane (usually called also the planck brane). The branes are postioned at y=0 and y=L and there is a Z₂-symmetry identification y <-> -y, y+L <->L-y. This relates, at least conceptually, this scenario to the Horava-Witten, as it will be shown later.

From this departure there are two models. The RS-2 model keeps the distance between branes finite. The RS-1 model sends the hidden brane to infinity (i.e. L->infinity) and it effectively behaves as if it would only have one brane. It is the bes suited for being related to AdS/CFT correspondence and an string realization based on flux (warped) compactifications of Type II B superstrings (ore Type II A related to them by mirror symmetry). There are however a few characteristics that this models share. One of them is that they solve the "hierarchy problem". Loosely speaking this problem consists in that the large difference of energy between the electroweak scale and the planck scale requires a very fine tunning of many constants. Supersimmetry could be a solution for this problem, but the Randall-sundrum models solve it in a different way. It can be shown that the energy of the particles in the planck brane is seen in the visible sector damped by the exponential factor of the metric. This automatically addresses the problem. This was, seemingly, the major goal of the first papers in the subject. This explains that the branes are plane Minkowsky space. This means that model is not a cosmologicla model. But there are possible additions which allows to convert it into a cosmological model, let´s say a few about it.

One thing that one would care about going into cosmological considerations is the cosmological constant. It can be seems that the visible brane has a positive tension (understood as self-gravity; in an "stringy" viewpoint it would be the brane tension, i.e. density of energy) while the hidden brane has a negative tension. The bulk, being a AdS, has a negative cosmological constant. The tensions of the branes compensate so the visible brane has a 0 cosmological constant. Introducing matter in the bulk it can get an small positive cosmological constant, but that requires a lot of fine tuning.

The inclusion of matter opens new perspectives. If we must go to a cosmological model we must have matter, and get an FRW scenario (to begin with). The inclusion of matter in this phenomenological model has a curious feature The standard model matter is confined to the branes by a delta function (which certainly is not a "first principles" way to proceed, but, ey it is a phenomenological model). I´ll not dwell into the details (you can find them, for example, in the article that Roy Marteens wrote in the subject for living reviews in relativity, available in the links section of this blog).I´ll simple state that it is actually possible to get an FRW metric.

My main interest here is to present the interplay between this "warped worlds) and string theory, but I can´t avoid to say a few things about two more characteristics of them. The two things are related to black holes.

The first, and most famous, is that the increase of gravity intensity for small distances own to the additional macroscopic dimension. This means that the threesold for the production of a black hole in a collision of particles is seriously reduced. In particular there is an small possibility that in the energy available to the LHC microblack holes could formate (and later evaporate by Hawking process). In fact in the Strings 2007 conferences Lisa-Randall was actually pessimistic about this possibility, but still there is an small window for it.

The other black hole issue is that the rate of evaporation of primordial black holes is modified, actually slowed down. by the extra dimension. In particular that means that most of the primordial black holes wouldn’t have evaporated (that explain why the gamma ray bust corresponding to the last moments of their existence have not been observed) and that the density of that black holes would be high (the probability of being one in the solar system being reasonably high). I must say that the mathematical description of a black hole in the brane worlds is a delicate issue and that it requires numerical calculations.

After heaving done a description of some aspects of the brane world universes let’s go to the Horava Witten theory. It consists of two steps. First one compatifies the theory in a S¹/Z(2) orbifold. Such and orbifold is a circle with the upper and inferior half identified that is, a segment. The extremes of the segment are fixed points under the action of the Z(2) group. This means that we have two ten dimensional plains and a 11 dimensional bulk. Requirements of cancellation of gravitational and gauge anomalies in the two orbifold plains require that they must implement an E(8)xE(8)symmetry, the same that most phenomenologically promising heterotic superstring theories. The ten dimensional planes must, actually, compactified into planck sized spaces (usually Calabi-Yaus). The details of the calculations involving anomalies predict a relation between the gauge coupling and the size of the eleventh dimension of the form:

2

Restrictions from cosmology imply that the size of the orbifold would be of the oorder of 10 times the planck size. This is a mayor departure form the RS models. Another thing is that the bulk, would, at least in the simplest models, supersymmetric, i.e. not AdS. Going beyond the "heuristic" description and getting actual effective equations for the model is not a trivial task, but it has been realized. From those equations it is possible to calculate which matter is actually available in the model. And one should try to get a FRW model from them. Well, one can get a hubble era with relativistic matter (i.e. matter at relativistic velocities) but it is now allowed to get non relativistic matter. In fact if one allows some modifications of the model, for example including M5 branes in the bulk, or similar nonperturbative effects to the low energy equations of motion, it could, perhaps, be possible to actually get non relativistic matter in the branes (I am not totally sure of which is the "last day" status of the question because most of the reviews that I have read in this topic are at most from the 2005).

I didn´t present all the details (it would be impossible in a blog sized post) but it is clear that although similar the RS models and the Horava Witten don´t fit totally. This has lead to different lines of research.. On one side there are the Stiendard-Turok Ekpyroctic model. This realizes, at least it is what they claims, very closely the Horava Witten model, but with a very significant diference. Instead of purchasing a FRW model they propose a ciclic model. They propose that form tiem to time (actually thousands mof millions of years) an M5 (or something similar) brane forms in the bulkd and is atracted towards the visible brane, where it desintegrtes resulting in a great increment of the energy which resembles similarities with an expanding universe but actually consist of separation of the particles (and creation of new ones own to the available energy). I didn´t read too much of this model so I can´t say much ore than this.

The other approach is to try to "enginer" RS scenaries form other tools of string theoy. For example one can do wrapped compactifications, as I mentioned at the begining. In that constrcuctioins the visible brane could be an stack of coincident branes. But not necessarilly D3-branes. They could be, for exampled, Dm-branes wraped around n dimesnional "supersymmetric" homological cicles of the compactifeid dimension (which result in a flux) or another constructions.The AdS/CFT correspondence that I have mentiones ocassionaly rquieres the existence (betwen the planck and the standard model branes) of a region many AdS radii in size.The RS sndrum scenario would be the strong coupling version of an older idea for solving the hierarchy problem. One startswith some ultraviolete fixed point CFT around the UV scale (planck scale) and perturbs it by a marginally relevant operator (whose is dimension is close to, say, 4 - ε) then one can naturally generate scales much lower than Mpl. The RG (renormalization group) runningof the couplings in the perturbed field theory is logaritmic, and therefore the relevant coupling will have sgnificant dynamical effects only afther a vast amount of RG running. The translation of this scenario to the RS models is via the AdS/CFT dictionary.


Describing, even "bloglike" the detaills would require another post. But I hope that with what I have told here the reader could get an overview of how goes the interplay betwen phenomenological models and more microscopic stringy considerations.

As a finall comment to sy that not all the string theorist are to conveiced that these secenaries are the most probably realized by nature. Neither it is probable that they would shide light into more fundamental problems of string theory. But what is clear that they have many intriguing posibilties, some of them which could connect to measurable effects and that it is reasonable that people work on them.