Había escrito, hace ya tiempo, una entrada sobre supersimetría, esta. Continuo el tema introduciendo una realización de dicha supersimetría en términos de un lagrangiano sencillo, lo que se conoce como el modelo de Wess-Zumino. Quien no tenga muy recientes sus conocimientos de teoría cuántica de campos, y en particular los tipos posibles de spinores, puede leer sobre ello en esta entrada de mi otro blog.
Este va a constar de dos campos, un campo escalar complejo $\phi$ formado por dos campos reales A y B, $\phi=(A+iB/\sqrt{2})$ y un campo spinorial de Majorana $\psi$. Ambos campos van a carecer de masa. El motivo para ello es que en la naturaleza no se ha observado la supersimetría, lo cuál indica que caso de existir, la supersimetría debe estar rota. Se supone que las partículas supersimétricas de las partículas conocidas habrán adquirido masa a trvés de un proceso de ruptura de esta supersimetría. Con estos ingredientes el término cinétco de nuestro lagrangiano será.
1. $ L= \partial^{\mu} \phi^*\partial_{\mu}\phi ~ + ~ 1/2i\bar\Psi\displaystyle{\not} \partial \Psi$
Ese lagrangiano es invariante bajo una tranformación SUSY global:
2. $\delta A=\bar\epsilon\psi $ $\delta B=i\bar \epsilon\gamma_5 \psi$
$\delta \psi=-i\gamma^\mu[\partial_\mu (A + i \gamma_5B)]\epsilon$
Donde $\epsilon$ es el generador infinitesimal (asumo que el lector esta familiarizado con como surgen los generadores infinitesimales de simetrías en mecánica cuántica y su relación con las simetrías globales a través de la exponenciación) de la supersimetría, un spinor infinitesimal de Majorana.
Puede verse que, como se espera de una supersimetría, esta transformación nos cambia campos bosónicos en campos fermiónicos. Para ser supersimétrica el lagrangiano debe ser invariante bajo esta transformación. Se puede verificar que bajo ese cambio la variación del lagrangiano es:
3. $ \delta L=\partial_\mu[1/2\bar\epsilon\gamma^\nu(\displaystyle{\not}\partial(A + i\gamma_5 B))\psi] $
Este $\delta L $ es una derivada total y por tanto no contribuye a la variación total de la acción y , como anunciaba, hace que 1 sea un lagrangiano supersimétrico. En general los lagrangianos supersimétricos no pueden ser invariantes bajo supersimetría, salvo que sean constantes, y siempre debe entenderse la invarianza en el sentido de que su variación es una derivada total.
Este lagrangiano es adecuado para partículas libres. Si añadimos interacciones se encuentra que le conmutador de dos transformaciones no es cerrado fuera de la capa de masas, y por tanto no es adecuado. Para paliar eso deben añadirse dos campos bosónicos extra, normalmente designados F y G, cuyo lagrangiano es:
4. $ L= 1/2F^2 + 1/2 G^2 $
La solución de la ecuación de Euler Lagrange asociada al lagrangiano 4 es F=G=0 y por tanto estos campos no tiene estados en la capa de masas, intervienen en la teoría sólo como partículas virtuales intermedias.
Se ha descrito hasta ahora como sería el lagrangiano para partículas sin masa. Nada impide construir el lagrangiano para partículas con masa. El término de masa tendria la forma:
5. $ L _m= m(FA + GB -1/2\bar\psi \psi) $
La forma mas general de un término de interacción -renormalizable sería.
6. $ L_i= g/\sqrt{2}[FA^2 - FB^2 + 2GAB - \bar\psi(A - i\gamma_5B)\psi] $
Este sería el modelo elemental de Wess-Zumino. Si uno pretende hacer teorías de campos supersimétricas realistas debería trabajar con fermiones quirales zurdos. No es especialmente complicado hacerlo, y repitiendo los pasos uno llegaría a una expresión de los lagrangianos anteriores en términos de esos fermiones quirales. El aspecto más interesante de ese desarrollo es que uno termina con un lagrangiano que puede expresarse de la forma:
7. $ L = L_K - |\partial W/\partial \phi|^2 ~ - ~ 1/2(\partial^2 W/\partial \phi^2\psi^T_L C \psi_L + herm.conj) $
Aquí $L_k$ sería el término cinético para los campos correspondientes y W sería lo que se conoce como el superpotencial. Este juega un papel importante en muchas discusiones sobre supersimetría y será tratado con mas detalle en ulteriores entradas. Por ahora decir que para el modelo sencillo que estamos considerando aquí su expresión más general sería:
8. $ W= 1/2m\phi^2 ~ + ~ 1/3 g\phi^3 $
En esta entrada se ha presentado el que posiblemente sea el tratamiento mas sencillo posible de la supersimetría. Actualmente es muy común usar el formalismo de supercampos. Este se basa en la noción de superespacio. El superespacio es el resultado de añadir a las componentes geométricas normales unas componentes "fermiónicas" representadas como variables de Grassman. Un supercampo dependería de ambos tipos de variables. Dadas las peculiares propiedades de las variables de grassman es muy sencillo ver que un desrrollo en serie en términos de las mismas es finito y que, por tanto, se puede dar una expresion general para un supercampo. Cuando se hace eso para campos que solamente tengan spin 1/2 y y 0 se puede ver que el modelo de supercampos obtenido es equivalente a el modelo de Wess-Zumino presentado aquí. Si además se impone que los campos fermiónicos sean quirale se obtiene la versión quiral del modelo de Wess-Zumino. El supercampo que cumple esas características es conocido cómo "supercampo quiral". Por supuesto se pueden hacer construcciones supersimétricas para campos gauge y, de ese modo, teorías gauge supersimétricas y análogos supersimétricos del modelo standard. La extensión supersimétrica mas sencilla de el modelo standard se conoce como MSSSM (minimal supersymetric stadard modell).
Aquí hemos tratado la supersimetría global. Cuando esta se hace local aparece de manera natural la gravitación y tendríamos teorias de supergravedad. Dado que la supersimétria no esta realizada en el modelo standard se asume que si el universo presenta supersimetría debe hacerlo en una versión con supersimetría rota. La ruptura de supersimetría es un tópico complejo, y juega un papel fundamental en la mayoria de modelos fenomenológicos que se postulan para extender el modelo standard de partículas. Indirectamente eso significa que también juegan un papel en las teorías de cuerdas, en sus diversas variantes. Por ejemplo la teoría F, la mas desarrollada a nivel fenomenológico utiliza una variante del mecanismo de supersimetría conocido como modelo de guidicce-massiero.
Se irán tratando esos tópicos en posteriores entradas.
Finalizo diciendo que estos posts siguen principalmente el libro de texto de P.D. B. Collins, A.D. Martin y E.J Squires "Particle physics and cosmology". A eso he añadido información adicional de los libros de M. Dine "Supersymmetry and superstrings" y el volumen III de el libro de teoría cuántica de campos de Steven Weinberg.
Tuesday, November 24, 2009
Saturday, October 31, 2009
The dark side of the landscape
In the previous post I had presented the multiverse in a way that made it look almost innocuous. As I have said a few times in this blog I had heard about how the landscape (existence of a large number of vacua) in string theory made it unavailable to make predictions.
Despite it the actual articles I had read didn't give to me that impression, so I suspected that I was missing something, the problem is that I didn't know what. Reading a recent entry in Lubos blog titled A small Hodge three-generation Calabi-Yau I faced again that problem of missing information. So I reared once again the KKTLT paper and I searched for bibliography that would give me some cloud.
At last I was lead to the correct paper, The statistics of string/M theory vacua by Michael R. Douglas (he is not the actor, of course). The abstract of the paper says all it:
We discuss systematic approaches to the classification of string/M theory vacua, and physical
questions this might help us resolve. To this end, we initiate the study of ensembles of
effective Lagrangians, which can be used to precisely study the predictive power of string
theory, and in simple examples can lead to universality results. Using these ideas, we outline
an approach to estimating the number of vacua of string/M theory which can realize
the Standard Model.
I still haven't finished to read the paper, but the image is clear. Yes, one can have a chaotic/eternal inflation scenario that creates an infinite of universes, or one can go from one to another thought some kind of CDL (Coleman de Luccia) or Hawkings instantons among deSitter vacua or whatever mechanism to create an universe for whatever vacua of the one available in string theory. An yes, every new universe would have an smaller cosmological constant that the previous one. In that way one has an universe with the small cosmological constant (cc) observed in ours. The anthropic principle (or ideology as prefer to name it Lubos) says that in universes with large cc there are no observers so it is not that bizarre that we observe such an small cc, despite the fact that naturally theories with broken supersymmetry would have a big one to begin with.
The real problem is that in that paper is argued that even with the restrictions of an small cc and the observed gauge content (the standard model one) one still has a large number of solutions with the values of the coupling constants, masses of the particles and etc. in the observed margin of the standard model. I have made quick search in the paper to see if it was here where it appeared the famous $10^{500}$ but I couldn't find it (the search feature of acrobat seems to not work with math expressions) but in the text appear ofthem $10^{100 }~ 10^{400}$ so it is in the right order of magnitude. I have intention of reading this paper soon, as well as another by Kallosh and Linde, Landscape, the scale of SUSY breaking, and inlation
It is not that I like the idea of the landscape, I don't, and that's why I hadn't found sooner this papers and I had searched other lines of investigations, such as the ones mentioned in this blog. But like it seems that cosmology is a such a hot topic nowadays, mainly because the large amount of data available, I think it is a good idea to know this kind of things in some detail.
As I had said previously, in other blog entries, I was aware that there were some concrete approaches that tried to disprove the landscape, understood in the sense presented here-that is, too many vacuums compatible with the standard model, not just too many vacuums compatible with an small cosmological constant-. Some of that papers are The String Landscape and the Swampland discussed by Lubos here and also discussed by Distler in his entry YOU CAN’T ALWAYS GET WHAT YOU WANT. More entries in Lubos blog discussing papers against the (SM)landscape are Ooguri and Vafa's swampland conjectures. He also has a paper with C. Vafa and Nima Arkani-Hamed titled The String Landscape, Black Holes and Gravity as the Weakest Force. I think that I have seen a blog entry of him about that paper, but it doesn't appear in the trackback for some reason.
Well, I leave this entry as a loosely discussed bibliography of the real problems of the landscape ideology. As I said there are possibly good reasons to expect a good "vacuum selection method" as M. Douglas calls it and so one wouldn't care too much about it. Possible the LHC could give a cloud of it. It is good to know that beams are beginning to circulate in it again, at least partially, and thatvry soon-if everything goes ok-it will be giving data.
Despite it the actual articles I had read didn't give to me that impression, so I suspected that I was missing something, the problem is that I didn't know what. Reading a recent entry in Lubos blog titled A small Hodge three-generation Calabi-Yau I faced again that problem of missing information. So I reared once again the KKTLT paper and I searched for bibliography that would give me some cloud.
At last I was lead to the correct paper, The statistics of string/M theory vacua by Michael R. Douglas (he is not the actor, of course). The abstract of the paper says all it:
We discuss systematic approaches to the classification of string/M theory vacua, and physical
questions this might help us resolve. To this end, we initiate the study of ensembles of
effective Lagrangians, which can be used to precisely study the predictive power of string
theory, and in simple examples can lead to universality results. Using these ideas, we outline
an approach to estimating the number of vacua of string/M theory which can realize
the Standard Model.
I still haven't finished to read the paper, but the image is clear. Yes, one can have a chaotic/eternal inflation scenario that creates an infinite of universes, or one can go from one to another thought some kind of CDL (Coleman de Luccia) or Hawkings instantons among deSitter vacua or whatever mechanism to create an universe for whatever vacua of the one available in string theory. An yes, every new universe would have an smaller cosmological constant that the previous one. In that way one has an universe with the small cosmological constant (cc) observed in ours. The anthropic principle (or ideology as prefer to name it Lubos) says that in universes with large cc there are no observers so it is not that bizarre that we observe such an small cc, despite the fact that naturally theories with broken supersymmetry would have a big one to begin with.
The real problem is that in that paper is argued that even with the restrictions of an small cc and the observed gauge content (the standard model one) one still has a large number of solutions with the values of the coupling constants, masses of the particles and etc. in the observed margin of the standard model. I have made quick search in the paper to see if it was here where it appeared the famous $10^{500}$ but I couldn't find it (the search feature of acrobat seems to not work with math expressions) but in the text appear ofthem $10^{100 }~ 10^{400}$ so it is in the right order of magnitude. I have intention of reading this paper soon, as well as another by Kallosh and Linde, Landscape, the scale of SUSY breaking, and inlation
It is not that I like the idea of the landscape, I don't, and that's why I hadn't found sooner this papers and I had searched other lines of investigations, such as the ones mentioned in this blog. But like it seems that cosmology is a such a hot topic nowadays, mainly because the large amount of data available, I think it is a good idea to know this kind of things in some detail.
As I had said previously, in other blog entries, I was aware that there were some concrete approaches that tried to disprove the landscape, understood in the sense presented here-that is, too many vacuums compatible with the standard model, not just too many vacuums compatible with an small cosmological constant-. Some of that papers are The String Landscape and the Swampland discussed by Lubos here and also discussed by Distler in his entry YOU CAN’T ALWAYS GET WHAT YOU WANT. More entries in Lubos blog discussing papers against the (SM)landscape are Ooguri and Vafa's swampland conjectures. He also has a paper with C. Vafa and Nima Arkani-Hamed titled The String Landscape, Black Holes and Gravity as the Weakest Force. I think that I have seen a blog entry of him about that paper, but it doesn't appear in the trackback for some reason.
Well, I leave this entry as a loosely discussed bibliography of the real problems of the landscape ideology. As I said there are possibly good reasons to expect a good "vacuum selection method" as M. Douglas calls it and so one wouldn't care too much about it. Possible the LHC could give a cloud of it. It is good to know that beams are beginning to circulate in it again, at least partially, and thatvry soon-if everything goes ok-it will be giving data.
Saturday, October 17, 2009
Universe or multiverse?
Universe or multiverse?
Recently there has been some peak of comments on the blogosphere about the multiverse, partially because of a new article by Linde and Vanchury titled How many universe are in the multiverse?.
But the battle against the multiverse, and it's buddy's, the anthropic principle and the string landscape are not new at all. Peter Woit is a championship of that cause. I have always considered P.W. as innocuous, and a source of information about string theory, even if he doesn't like it. Being he a mathematician, or at most a mathematical physicist it is not a lack of respect to his position in an university to not take seriously their objections to a branch of physics that he mostly doesn't understand.
But recently I am beginning to think that in fact he can be causing some damage. The problem I see is that he is so intended to criticise string theory that he only search the part that is good for his purposes without worrying of understanding the whole picture. Worse still, he can make believe that his biased view is the whole view. And that's very bad because it gives a very wrong perspective of what is being done in string theory, and in cosmology and high energy physics in general.
In particular what he says about multiverse, string landscape and similar topics is totally misleading. I am not saying that these are not conflictive areas. Only that what Woit says about them is not representative. To begin with one may realize that the existence of multiverses is, in some cases, inflation, mostly a consequence of already proved physicist with the only assumption of some special issues on he potential of the inflaton. Also, if one trust string theory, the multiverses would rise as a consequence of a saltatory cosmological constant. In fact that two scenarios are similar in spirit, although very different in the details.
If a reader of this blog would want to get a much better idea I would recommend him the reading of the book presented at the beginning of this entry. IT is edited by Bernard Card, who also makes a presentation chapter and thematic one, "the anthropic principle revisited". The firs chapter gives an overview of the rest of the book and explains the many meanings of the term "multiverse" that are treated.
The book itself is bases in a series of conferences partially supported by the templeton foundation. The list of participants includes a list of very prominent physicist such as S. Weinberg, S. Hawkings, L. Susskind,A. Linde, P. Davies, R. Kallosh and a long etc. The list of topics is also very broad, covering many of the variants of the multiverse idea and why it raises in nowadays physics research.
I only have read a few (six) part of the articles and I am alternating them with other articles about inflation in string theory, supersymmetry breaking and general literature about the cosmological constant. My idea is that probably there are better alternatives for the apparent existence of an accelerated universe (and in general, possibly, for some fine tunning problems) but that it would be stupid not to read (at least a part of) what appears in that book if ones is concerned about it.
Monday, September 28, 2009
Collisions of universes
The arxiv blog took notice of an article about the possible existence ofo experimental evidence of the collision of universes. You can read it here.
For those people who has read the conventional cosmological sceneries, that is, a FRW type cosmology, slightly corrected by a very tiny cosmological constant and an early period of inflation the idea of many universes could sound to them very speculative. and probably the could immediately think that it is based on that "evil string theorists" inventions.
In these last dates my readings in theoretical physics have been mainly related to cosmology. I have learned that the most extended idea of the multiple universes is rooted in the "eternal inflation" and also by the alternative idea of "chaotic inflation". Those are inventions of cosmologists and not of string theorists, although the last ones have got the idea, merged it with ideas of Weinberg and the Bethe-Theitleboin mechanism and implemented it in stirng theory leading to the bousso-Polchinsky proposal, the KKLT realization of it and in last instance the whole odea of the landscape.
But, basically the idea of eternal inflation is independent of string theory. If one takes seriously the problem of the vacuum energy in QFT one is faced with the problem that this is of the order of the supersymmetry breaking (if one doesn't belive in supersymmetry one would have the planck energy). That energy would led to a very fast expansion of the universe when part of it is released by transition to a level with less energy. The whole thing is that that transition would not be simultaneous on all points. Then one would have an expanding universes coexisting with an stationary one. The expanding universes could, agian, suffer another phase transition to a less energetic vacuum, resulting in new expanding universe. and so on, in a nested proccess. This is, roughly speaking, the idea of "bubble nucleation" that I have mentioned sometimes in this blog without too many explanations.
Ideally that universes would be disconnected and couldn't collide. That paper on arxiv investigate the opposite possibility.
One consequence of eternal inflation is the possibility that there would be an infinite number of universes. Taking account of the fact that here are a limited number of configurations that results in the need that every event , and it's variants would happen an infinite of times. It is a variant, for practical purposes, of the Everet's "many worlds" interpretation of quantum mechanics.
Well, if in some way one could us that infinite worlds variants amazing things could happen. In fact some people propose seriously that quantum computers make basically that. They would be many copies of the same computer, but in different universes, every one doing an independent calculation. Some people even try to relate the quantum and the eternal inflation into a single mechanism.
All this is very CF like. I remember the film "the unique" by the martial arts star Jet Li. There the protagonist kills his copies in the other universes and recipes it's strength and knowledges.
If insome wya I could use that many worlds doubles I could read in detaillthis paper about a new proposal of unified theories, somewhat in the line of the everybody favourite surfer physicist. A superficial reading seems to suggest that the proposal is most satisfactory but I am skeptic about it.
Also I could read some other interesting papers in arxiv today, and advance with my own ideas faster. And I could write the article, in Spanish, about F-theory. In fact I am reading some further papers about F-theory and I'll wait a little bit before writing that entry.
Besides reading physics/maths I could dedicate more time to touch piano, to make some amateur composition of electronic music, to practice more hours in the week martial arts, and make also other sport activities. And I still would have time to read more CF books, go cinema, and etc, etc. But lacking that technology a most likely possibility would be to win some random game (euromillion or similar) and in that way I wouldn't have to waste time in "economic activities" (althought fortunately sometimes this overlap with my research/academic activities).
But even in the worst of cases I guess that I am going to have more time to dedicate to the blogs and think that there are a good bunch of interesting themes to write about.
For those people who has read the conventional cosmological sceneries, that is, a FRW type cosmology, slightly corrected by a very tiny cosmological constant and an early period of inflation the idea of many universes could sound to them very speculative. and probably the could immediately think that it is based on that "evil string theorists" inventions.
In these last dates my readings in theoretical physics have been mainly related to cosmology. I have learned that the most extended idea of the multiple universes is rooted in the "eternal inflation" and also by the alternative idea of "chaotic inflation". Those are inventions of cosmologists and not of string theorists, although the last ones have got the idea, merged it with ideas of Weinberg and the Bethe-Theitleboin mechanism and implemented it in stirng theory leading to the bousso-Polchinsky proposal, the KKLT realization of it and in last instance the whole odea of the landscape.
But, basically the idea of eternal inflation is independent of string theory. If one takes seriously the problem of the vacuum energy in QFT one is faced with the problem that this is of the order of the supersymmetry breaking (if one doesn't belive in supersymmetry one would have the planck energy). That energy would led to a very fast expansion of the universe when part of it is released by transition to a level with less energy. The whole thing is that that transition would not be simultaneous on all points. Then one would have an expanding universes coexisting with an stationary one. The expanding universes could, agian, suffer another phase transition to a less energetic vacuum, resulting in new expanding universe. and so on, in a nested proccess. This is, roughly speaking, the idea of "bubble nucleation" that I have mentioned sometimes in this blog without too many explanations.
Ideally that universes would be disconnected and couldn't collide. That paper on arxiv investigate the opposite possibility.
One consequence of eternal inflation is the possibility that there would be an infinite number of universes. Taking account of the fact that here are a limited number of configurations that results in the need that every event , and it's variants would happen an infinite of times. It is a variant, for practical purposes, of the Everet's "many worlds" interpretation of quantum mechanics.
Well, if in some way one could us that infinite worlds variants amazing things could happen. In fact some people propose seriously that quantum computers make basically that. They would be many copies of the same computer, but in different universes, every one doing an independent calculation. Some people even try to relate the quantum and the eternal inflation into a single mechanism.
All this is very CF like. I remember the film "the unique" by the martial arts star Jet Li. There the protagonist kills his copies in the other universes and recipes it's strength and knowledges.
If insome wya I could use that many worlds doubles I could read in detaillthis paper about a new proposal of unified theories, somewhat in the line of the everybody favourite surfer physicist. A superficial reading seems to suggest that the proposal is most satisfactory but I am skeptic about it.
Also I could read some other interesting papers in arxiv today, and advance with my own ideas faster. And I could write the article, in Spanish, about F-theory. In fact I am reading some further papers about F-theory and I'll wait a little bit before writing that entry.
Besides reading physics/maths I could dedicate more time to touch piano, to make some amateur composition of electronic music, to practice more hours in the week martial arts, and make also other sport activities. And I still would have time to read more CF books, go cinema, and etc, etc. But lacking that technology a most likely possibility would be to win some random game (euromillion or similar) and in that way I wouldn't have to waste time in "economic activities" (althought fortunately sometimes this overlap with my research/academic activities).
But even in the worst of cases I guess that I am going to have more time to dedicate to the blogs and think that there are a good bunch of interesting themes to write about.
Thursday, August 13, 2009
Recently on arxiv
Summertime, holidays, nothing important going on, isn't it?
Maybe, but in my opinion some recent papers on arxiv are interesting.
I am going to begin by CYBERsusy. The name can suggest some SF novel cyberpunk heroine. But not. It is an acronym for 'CohomologicallY Broken Effective Retro SUperSYmmetry'. The article is titled A new mechanism for supersymmetry breaking
in the Supersymmetric Standard Model.
To break supersymmetry is a good thing and a new mechanism to do so sounds important. If, moreover, the abstract ends with "The theory also leads to a zero cosmological
constant after SUSY breaking." one could begin to feel seriously interested. Being so it was a bit amazing to see how it passed unnoticed in the "big guys" blogs (you know who they are ;-) ). So I investigated a bit and I found this old entry by Lubos: Dixon law firm: CyberSUSY.
I also found that there is a blog mantained by Jon Dixon in the theme, John Dixon: Cohomology, supersymmetry and cybersusy
Well, the Lubos article refers to an older version of the theory, maybe the new one has corrected the fails, but I guess that not too much.
Another paper that I have found intriguing is related to the cosmological constant and the expanding universe. It is this, Does Unruh radiation accelerate the universe? A novel approach to the cosmic acceleration" and it's arxiv. This is the abstract:
We present a novel mechanism for the present acceleration of the universe. We find that the temperature of the Unruh radiation perceived by the brane is not equal to the inherent temperature (Hawking temperature at the apparent horizon) of the brane universe in the frame of Dvali-Gabadadze-Porrati (DGP) braneworld model. The Unruh radiation perceived by a dust dominated brane is always warmer than the brane measured by the geometric temperature, which naturally induces an energy flow between bulk and brane based on the most sound thermodynamics principles. Through a thorough investigation to the microscopic mechanism of interaction between bulk Unruh radiation and brane matter, we put forward that an energy influx from bulk Unruh radiation to the dust matter on the brane accelerates the universe
Well, the two last papers were authored by a Lubos discredited physicist in one case and by a not well known Chinese team in the other so One can find reasonable to see no resemblance of them.
More surprising are the two next papers.
The first one is by mr. Brian "elegant universe" Green and coauthores by Daniel Kabat1;2y and Stefanos Marnerides. The title sound interesting, "Dynamical decompactication and Three Large Dimensions". The actual paper is this and this is the abstract:
We study string gas dynamics in the early universe and seek to realize the Brandenberger-
Vafa mechanism{a goal that has eluded earlier works{that singles out three or fewer
spatial dimensions as the number which grow large cosmologically. To this end, we
consider a dilute gas of strings on a large torus, so that strings typically interact at significant impact parameters. A strong exponential suppression in the interaction rates for d > 3 spatial dimensions rejects the classical argument that string worldsheets generically only intersect in four or fewer spacetime dimensions. As a consequence of this suppression, a scan over initial conditions establishes that in the dilute regime
decompactication of d = 3 spatial dimensions is favored over d > 3.
Nowadays the trend seems to be bottom-up approaches where one consider the standard model as an input and looks for stringy constructions to implement it in a coherent way (this goes for intersecting brane worlds and for F-theory GUT's). But I think that still is very interesting to see how "natural" is to have a world with three macroscopic dimensions and this papers seems a good approach to answer that question.
There is another paper authored by two very well known string theorists, Joseph Polchinski and Eva Silverstein. It is this: Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT.
Because my knowledge of the AdS/CFT is still limited to it's basics, the chapters in the Becker-Becker-Schwartz and Clifford Johnson books plus a not too successful reading of a few reviews I can't say too much about the relevance of the paper. But still it sounds important and I am surprised not to have read about it in the you know who blogs. Maybe it is just a question of time, who knows.
The last paper I'll link is this: The Search for a Realistic String Model at LHC The title is self-explanatory. The authors are well known people, James A. Maxin, Van E. Mayes, D.V. Nanopoulos (well, actually the last one is well known for sure).
It is about the construction of a realistic intersecting D-brane model. At first sight one could think that with the rise of the F-theory GUT models the interest on this kind of phenomenological approaches would have become somewhat outdated, but seemingly it is not the case. Possibly one of the reason is that there is a lot of literature on the subject of seeking signatures of this kind of models in the LHC. You can find many of the articles doing a search for "string hunters" on arxiv hep-th. As you can see recently there was a paper on that subject, "The LHC string hunters companion II". I am actually reading the paper that correspond to the first part. It is very illustrative on how the Randall-Sundrum sceneries are actually achieved in fully string compactifications through branes wrapped in "Swiss chase" Calabi-Yau manifolds. And it contain a lot of formulae for cross sections. I think that It can be useful to me if at last my idea about a tired light mechanism to explain the observations interpreted as accelerated universe expansion make any sense after all. Independently of that they are possibly the "state of the art" in string phenomenology out of the F-Theory GUT's and (M-)heterotic models. Possibly I'll make a dedicated post to this intersecting brane models some day. But for now I think that the reader already has a lot of papers to search for.
Maybe, but in my opinion some recent papers on arxiv are interesting.
I am going to begin by CYBERsusy. The name can suggest some SF novel cyberpunk heroine. But not. It is an acronym for 'CohomologicallY Broken Effective Retro SUperSYmmetry'. The article is titled A new mechanism for supersymmetry breaking
in the Supersymmetric Standard Model.
To break supersymmetry is a good thing and a new mechanism to do so sounds important. If, moreover, the abstract ends with "The theory also leads to a zero cosmological
constant after SUSY breaking." one could begin to feel seriously interested. Being so it was a bit amazing to see how it passed unnoticed in the "big guys" blogs (you know who they are ;-) ). So I investigated a bit and I found this old entry by Lubos: Dixon law firm: CyberSUSY.
I also found that there is a blog mantained by Jon Dixon in the theme, John Dixon: Cohomology, supersymmetry and cybersusy
Well, the Lubos article refers to an older version of the theory, maybe the new one has corrected the fails, but I guess that not too much.
Another paper that I have found intriguing is related to the cosmological constant and the expanding universe. It is this, Does Unruh radiation accelerate the universe? A novel approach to the cosmic acceleration" and it's arxiv. This is the abstract:
We present a novel mechanism for the present acceleration of the universe. We find that the temperature of the Unruh radiation perceived by the brane is not equal to the inherent temperature (Hawking temperature at the apparent horizon) of the brane universe in the frame of Dvali-Gabadadze-Porrati (DGP) braneworld model. The Unruh radiation perceived by a dust dominated brane is always warmer than the brane measured by the geometric temperature, which naturally induces an energy flow between bulk and brane based on the most sound thermodynamics principles. Through a thorough investigation to the microscopic mechanism of interaction between bulk Unruh radiation and brane matter, we put forward that an energy influx from bulk Unruh radiation to the dust matter on the brane accelerates the universe
Well, the two last papers were authored by a Lubos discredited physicist in one case and by a not well known Chinese team in the other so One can find reasonable to see no resemblance of them.
More surprising are the two next papers.
The first one is by mr. Brian "elegant universe" Green and coauthores by Daniel Kabat1;2y and Stefanos Marnerides. The title sound interesting, "Dynamical decompactication and Three Large Dimensions". The actual paper is this and this is the abstract:
We study string gas dynamics in the early universe and seek to realize the Brandenberger-
Vafa mechanism{a goal that has eluded earlier works{that singles out three or fewer
spatial dimensions as the number which grow large cosmologically. To this end, we
consider a dilute gas of strings on a large torus, so that strings typically interact at significant impact parameters. A strong exponential suppression in the interaction rates for d > 3 spatial dimensions rejects the classical argument that string worldsheets generically only intersect in four or fewer spacetime dimensions. As a consequence of this suppression, a scan over initial conditions establishes that in the dilute regime
decompactication of d = 3 spatial dimensions is favored over d > 3.
Nowadays the trend seems to be bottom-up approaches where one consider the standard model as an input and looks for stringy constructions to implement it in a coherent way (this goes for intersecting brane worlds and for F-theory GUT's). But I think that still is very interesting to see how "natural" is to have a world with three macroscopic dimensions and this papers seems a good approach to answer that question.
There is another paper authored by two very well known string theorists, Joseph Polchinski and Eva Silverstein. It is this: Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT.
Because my knowledge of the AdS/CFT is still limited to it's basics, the chapters in the Becker-Becker-Schwartz and Clifford Johnson books plus a not too successful reading of a few reviews I can't say too much about the relevance of the paper. But still it sounds important and I am surprised not to have read about it in the you know who blogs. Maybe it is just a question of time, who knows.
The last paper I'll link is this: The Search for a Realistic String Model at LHC The title is self-explanatory. The authors are well known people, James A. Maxin, Van E. Mayes, D.V. Nanopoulos (well, actually the last one is well known for sure).
It is about the construction of a realistic intersecting D-brane model. At first sight one could think that with the rise of the F-theory GUT models the interest on this kind of phenomenological approaches would have become somewhat outdated, but seemingly it is not the case. Possibly one of the reason is that there is a lot of literature on the subject of seeking signatures of this kind of models in the LHC. You can find many of the articles doing a search for "string hunters" on arxiv hep-th. As you can see recently there was a paper on that subject, "The LHC string hunters companion II". I am actually reading the paper that correspond to the first part. It is very illustrative on how the Randall-Sundrum sceneries are actually achieved in fully string compactifications through branes wrapped in "Swiss chase" Calabi-Yau manifolds. And it contain a lot of formulae for cross sections. I think that It can be useful to me if at last my idea about a tired light mechanism to explain the observations interpreted as accelerated universe expansion make any sense after all. Independently of that they are possibly the "state of the art" in string phenomenology out of the F-Theory GUT's and (M-)heterotic models. Possibly I'll make a dedicated post to this intersecting brane models some day. But for now I think that the reader already has a lot of papers to search for.
Tuesday, August 04, 2009
TGD in vixra
At last the pdf articles of Matti pitkanen about topological geometrodynamics have been uploaded to vixra.
If someone wants to beguin he would read Topological Geometrodynamics: Overview. Advise, despite the "overview" word in the title that pdf has 1000+ pages.
There are many other papers that the reader can find by himself in vixra.
I am aware that TGD is considered crackpot. For example Lubos said in a recent post (not specifically about TGD) that TGD only existed in Matti Pitkanen's imagination. Maybe, but I think that Matti is a nice smart guy, with a correct behaviour, and he deserves the right that someone with an accredited academic position claiming that TGD is crackpot would do a proper debunking of TGD (a reasonable part of it, it is not necessary to debug the whole 1000+ paper).
But surely I am not the right person to do such a debunking. Instead I'll debug in a separate post another paper in vixra, The Graviton Background Vs. Dark Energy. The abstract says:
In the model of low-energy quantum gravity by the author, cosmological redshifts are caused by interactions of photons with gravitons. Non-forehead collisions with gravitons will lead to an additional relaxation of any photonic flux. It gives a possibility of another interpretation of supernovae 1a data. Every massive body would be decelerated due to collisions with gravitons that may be connected with the Pioneer 10 anomaly. This mechanism needs graviton pairing and "an atomic structure" of matter for working it. Also an existence of black holes contradicts to the equivalence principle: any black hole should have a gravitational mass to be much bigger - about three orders - than an inertial one.
As the readers of this blog can deduce the author of this paper is presenting a TLT (tired light theory) as a replacement of the big bang. And the will remember that I had being considering the possibility that a TLT mechanism could be used to give and explanation of the supernovae data that is being interpreted as evidence of an accelerated expansion of the universe. I have developed a little bit more my ideas and I am not sure if they work, but as far as I see what that article says makes not special sense. I'll try to explain why in the next post.
If someone wants to beguin he would read Topological Geometrodynamics: Overview. Advise, despite the "overview" word in the title that pdf has 1000+ pages.
There are many other papers that the reader can find by himself in vixra.
I am aware that TGD is considered crackpot. For example Lubos said in a recent post (not specifically about TGD) that TGD only existed in Matti Pitkanen's imagination. Maybe, but I think that Matti is a nice smart guy, with a correct behaviour, and he deserves the right that someone with an accredited academic position claiming that TGD is crackpot would do a proper debunking of TGD (a reasonable part of it, it is not necessary to debug the whole 1000+ paper).
But surely I am not the right person to do such a debunking. Instead I'll debug in a separate post another paper in vixra, The Graviton Background Vs. Dark Energy. The abstract says:
In the model of low-energy quantum gravity by the author, cosmological redshifts are caused by interactions of photons with gravitons. Non-forehead collisions with gravitons will lead to an additional relaxation of any photonic flux. It gives a possibility of another interpretation of supernovae 1a data. Every massive body would be decelerated due to collisions with gravitons that may be connected with the Pioneer 10 anomaly. This mechanism needs graviton pairing and "an atomic structure" of matter for working it. Also an existence of black holes contradicts to the equivalence principle: any black hole should have a gravitational mass to be much bigger - about three orders - than an inertial one.
As the readers of this blog can deduce the author of this paper is presenting a TLT (tired light theory) as a replacement of the big bang. And the will remember that I had being considering the possibility that a TLT mechanism could be used to give and explanation of the supernovae data that is being interpreted as evidence of an accelerated expansion of the universe. I have developed a little bit more my ideas and I am not sure if they work, but as far as I see what that article says makes not special sense. I'll try to explain why in the next post.
Tuesday, July 28, 2009
Easy latex on blogpsot
I had said that I wanted an easy way to use latex on blogspot. Untill now I was using an external mimetex server and using the html img tag with the url of the mimetex cg and latex code in it. The idea was to create some kind of customized tag that would write the html code. That has too good points. On one hand it makes the edition of the post easier. On the other if the mimetex cg is changed you only need the link of the cgi in the script code that is asociated to the tag.
In order to do so I have tried to study the blogspot templates structure, but I have not found too usefull information. Most that I hve found is concerning the look of the blog and I am not too interested in that kind of things. I have tried to see if I could create tags, but I have not found too much info. I have made an easy javascript function, but it was not of too much help.
Fortunately I have found someone who made the work for me. You can read how to here. As you can read there once you add a personalized javascript gadget to your blog you can insert your latex code inside two dollar symbols and it its replaced by the right latex image when you publish the entry.
The code behind the scenes is this. I have not had time to study it. If you follow the stepts indicated in the webpage I linked before that javascript is called from a remote .js file and you can't customize it. Obvioulsly one could write the whole javascript code in the customized gadget or create your own copy of the js file whereever you want and customize it.
One bad aspect of the latex, as I use it in this blog, is that the images have some annoying borders, as you can see:
$$E=mc^2$$
I think that this problem can be advoided doing some CSS to create some tag for latex images but that is something that I'll do sometime later. Also I would like to study that javascript to use the wordpress tag for wrting latex, $latex the code goes here $ instead of the tow dolar symbols, in order to improve the crosscompatibility betwen blogspot and wordpress. But, anyway, that are minor questions, the hard problem is solved. Now it only remains that I would post about physics and write the equations, of course ;-).
In order to do so I have tried to study the blogspot templates structure, but I have not found too usefull information. Most that I hve found is concerning the look of the blog and I am not too interested in that kind of things. I have tried to see if I could create tags, but I have not found too much info. I have made an easy javascript function, but it was not of too much help.
Fortunately I have found someone who made the work for me. You can read how to here. As you can read there once you add a personalized javascript gadget to your blog you can insert your latex code inside two dollar symbols and it its replaced by the right latex image when you publish the entry.
The code behind the scenes is this. I have not had time to study it. If you follow the stepts indicated in the webpage I linked before that javascript is called from a remote .js file and you can't customize it. Obvioulsly one could write the whole javascript code in the customized gadget or create your own copy of the js file whereever you want and customize it.
One bad aspect of the latex, as I use it in this blog, is that the images have some annoying borders, as you can see:
$$E=mc^2$$
I think that this problem can be advoided doing some CSS to create some tag for latex images but that is something that I'll do sometime later. Also I would like to study that javascript to use the wordpress tag for wrting latex, $latex the code goes here $ instead of the tow dolar symbols, in order to improve the crosscompatibility betwen blogspot and wordpress. But, anyway, that are minor questions, the hard problem is solved. Now it only remains that I would post about physics and write the equations, of course ;-).
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