Ok, everybody made speculations about the meaning of the F in F-theory. Possibly the most accepted one was that it was due to Cumrumm Va(F)a. But an article appearing now in arxiv has shown it's real origin.
The authors of the article are Adil Belha and Leila Medari. It is titled "Superstrings, Phenomenology and F-theory". the abstract reads:
We give brief ideas on building gauge models in superstring theory, especially the four-dimensional models obtained from the compactification of F-theory. According to Vafa, we discuss the construction of F-theory to approach non-perturbative aspects of type IIB superstring. Then, we present local models of F-theory, which can generate new four-dimensional gauge models with applications to phenomenology.
It is based on invited talks given by A. Belhaj in Oviedo, Rabat, Zaragoza.
Untill here nothing seems to support my claim of the explanation of the origin of the name. But if you go and see the paper, available in: http://arxiv.org/pdf/0912.5295 one finds that it is written in French. That explains all it ;-).
Fortunately I have a relatively good knowledge of French and I could make a quick reading of the article. It is a good introduction to the topic, from the very beguining explaining the basics of string theory, D-branes and all that. Later it explains the basics of F-theory, of local models and of local F-theory GUT models. All of it in a short article of 15 pages.
Despite the name it doesn't dive too much into phenomenology. But still it gives a good introduction to many aspects of the subject for non initiated people. In that sense it is far better than the blog entry of Jackes Distler about the first big paper of Vafa. And, definitively, it looks like a good chance for Spanish people people interested in the subject but not speaking English and maybe speaking French.
By the way, for those that didn't read the Spanish entry about the CDMS announcement just say that F-theory GUTS predicts that the LSP (lightest supersymmetric partner) is the gravitino, which is not a viable candidate for a WIMP. The CDMS two events finding (irrespective of how statistically significant it could be) is kind of a hint that the LSP is a WIMP (maybe a neutralino) so if confirmed the actual Vafa models of F-theory GUT would become invalidated. Possibly the experts on the subject could recook some aspects of the more phenomenological aspects of the theory (mainly the supersymmetry breaking mechanism) to fit the new data. But certainly the best aspect of the whole construction, reproducing the standard model and make concrete predictions, would go away.
But, as Vafa said in the strings 2009 conferences. That's the bad point of making predictions, that they could be invalidated.
If someone is interested in knowing it I must say that since the CDMS announcement I have decided to study in more detail what heterotic phenomenology can offer. It doesn't mean that F-theory is not interesting any more, but irrespectively of the CDMS I needed to pay more attention to heterotic theories. The CDMS is just a good excuse.
Also I am reading (and in some cases rereading) a lot of articles in black holes (stringy and not stringy ones). You can read about it in my other blog (if you speak Spanish). Still I guess that I will also talk about the subject in this blog in a near future, when I have finished reading carefully a few bunch of articles. For example, today there is an article about the subject of B-h creation in particle collisions: http://arxiv.org/abs/0912.5481.
Other interesting articles today in arxiv are: Unification of Residues and Grassmannian Dualities by Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo and Jaroslav Trnka. The article continuate the MHV program to give a twistorial technique to find scattering amplitudes. I must admit that although I recognize it's interest I am not following too much that developments. Still I think some readers can find it more attractive than me.
Also I would note two papers in dark energy:
Inverse problem - reconstruction of dark energy models
Abstract:
We review how we can construct the gravity models which reproduces the arbitrary development of the universe. We consider the reconstruction in the Einstein gravity coupled with generalized perfect fluid, scalar-Einstein gravity, scalar-Einstein-Gauss-Bonnet gravity, Einstein-$F(G)$-gravity, and $F(R)$-gravity. Very explicit formulas are given to reconstruct the models, which could be used when we find the detailed data of the development of the universe by future observations. Especially we find the formulas using e-foldings, which has a direct relation with observed redshift. As long as we observe the time development of the Hubble rate $H$, there exists a variety of models describing the arbitrary development of universe.
The F(R) theories of the subject refers to approaches where one consider gravity theories with terms in the lagrangian that contain higher order terms in the curvature that appear as counterterms in the renormaliztion program of conventinal quantum gravity (the theory actually is not enormalizable because of the need of infinite diferent terms). There was recently a good review article about the subject and if I have time to read it I will post about that kind of theories.
Also about dark energy is a paper by A. M. Polyakov: Decay of Vacuum Energy .
Abstract:
This paper studies interacting massive particles on the de Sitter background. It is found that in some cases (depending on even/odd dimensionality of space, spins, masses and couplings of the involved particles etc) the vacuum acts as an inversely populated medium which is able to generate the stimulated radiation. This "cosmic laser" mechanism depletes the curvature and perhaps may help to solve the cosmological constant problem. The effect is more robust in the odd dimensional space-time, while in the even case additional assumptions are needed.
Polyakov is a very original thinker, and despite that sometimes it's ideas seems a bit non conventional it always worth reading him.
Possibly there are more interesting papers in axiv today, but I'll stop here.
Good new year to all readers.
Showing posts with label F-theory. Show all posts
Showing posts with label F-theory. Show all posts
Thursday, December 31, 2009
Wednesday, July 08, 2009
F-theory GUT for non experts
I have found a few papers that do a good job explaining the basics of F-theory in a relatively easy way. I could have posted them as un update of the previous post on the subject but I think it deserves an small separated post.
One paper is : F-theory, GUTs and Chiral Matter.
Another one, written by Hackman and Vafa is: From F-theory GUTs to the LHC
Also I think that the interested reader would try to understand more basic settings, previous to the F-theory revolution. I am talking about the intersecting branes scenarios. A short and good review is: Progress in D-brane model building.
The reason to investigate the last paper is that I find it is interesting to understand how one calculate family numbers, how chiral fermions arise and so that in more conventional D-brane models. In fact the firs paper I cite makes a good job explaining some of that aspects, but still.
Also I recommend, once again, the original paper of Ibañez, Quevedo et all in local models D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model. I have finished to read it and I find it very clear. As a plus it also has a brief chapter about F-theory.
Certainly the last papers about D-brane model building are not required to understand the F-theory ones, but It is good to understand what existed previously to better understand the goodness of the new. In that sense the papers recommended in my entry about the prehistory of F-theory GUTS are also valuables and focuses in diferent aspects than the ones cited here.
Anyway, if someone only wants a quick, but accurate, idea of the subject the two papers cited at the start of the post make a wonderful work
One paper is : F-theory, GUTs and Chiral Matter.
Another one, written by Hackman and Vafa is: From F-theory GUTs to the LHC
Also I think that the interested reader would try to understand more basic settings, previous to the F-theory revolution. I am talking about the intersecting branes scenarios. A short and good review is: Progress in D-brane model building.
The reason to investigate the last paper is that I find it is interesting to understand how one calculate family numbers, how chiral fermions arise and so that in more conventional D-brane models. In fact the firs paper I cite makes a good job explaining some of that aspects, but still.
Also I recommend, once again, the original paper of Ibañez, Quevedo et all in local models D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model. I have finished to read it and I find it very clear. As a plus it also has a brief chapter about F-theory.
Certainly the last papers about D-brane model building are not required to understand the F-theory ones, but It is good to understand what existed previously to better understand the goodness of the new. In that sense the papers recommended in my entry about the prehistory of F-theory GUTS are also valuables and focuses in diferent aspects than the ones cited here.
Anyway, if someone only wants a quick, but accurate, idea of the subject the two papers cited at the start of the post make a wonderful work
Thursday, June 04, 2009
String theory is good for...phenomenology of particle physics
Yesterday the number of visits to this blog had a major increase. Most of the traffic came from this post in Miguis web/blog.
The post was a translation to Spanish of an article in new scientist about the good points of string theory. I had seen a discussion of that article in Lubos blog, concretely here.
Well, that article comes to say that string theory is nowadays a good theory because it´s math structure, through the AdS/CFT correspondence is useful in QCD and condensed matter physics. Well, I don't know too much about that applications but if the experts in that subjects say so is a good sign.
But, actually, I don't think that that image is quite right nowadays. Readers of this blog know that I have played attention to many alternative theories. Some of the proponents of that theories make claims against string theory. Others, who don't actually offer any theory, that is, Peter Woit, claims that string theory "makes no predictions". In his blog he usually bring attention mostly to the most speculative articles written by string theorists.
Well, I am following, as much as I can, the actual F-theory minirevolution. Doing so I have become very surprised, and impressed, by how close string theory has become of actual physics. Before going into it I must say that I somewhat understand the sceptics in string theory. If one reads the books on the subject one certainly gets the impression that actual predictions are far away. For example the 1999 (that is, not too old) book of Michio Kaku Introduction to superstrings and M-theory in its chapters about phenonenology show the results of heterotic compactifications. In that results the best one could get were the standard model plus some additional U(1) factors. Also it was stated that to achieve the right number of generations , given by n=1/2X(Cy), that is, one half of the Euler characteristic of the Calabi-Yau mainfold, was difficoult (if not almost impossible).
Other books, as Polchinsky´s two volumes book and the Clifford Jones "D-branes" don't say too much about realistic compactifications. There are good reasons for that. The books are mostly concerned about the D-brane revolutions and its consequences, the black hole entropy calculation and the AdS/CFT conjecture. The most recent book of Becker-Becker-Schwartz makes more in deep cover of compactifications. But , with a good criteria, somewhat cares more about technical issues such as the moduli space of the compactification, mirror symmetries among type II A and type II B, and flux compactifications, which are relevants for the very important issue of moduli stabilization and the KKLT like models (related to the landscape). And , of course, the all make introductions to dualities, M theory, and , to a least extent, F-theory.
In fact all that are important technical aspects, and it requires time to learn them (one must read some articles if he really wants to properly understand some aspects). But one gets the impression that everything is still to far from LHC phsyics and cosmology testable predictions. In fact there is a very recent book, by a Michel Dine which goes into phenomenology title "supersymmetry and superstrings". I must say that I find that book somewhat failed. It is to brief covering subjects that even with some previous knowledge are hard to appreciate properly.
Well, in definitive, a lot of text books and no a clear signal of actual testable physics. Certainly discouraging. Divulgative books are not too different. That, certainly, can explain why some people has the impression that string theory is far from it's objectives. Blogs from string theorists try to say, to whoever listen them, that string theory is "the only game in town". In fact there are not many blogs in string theory with a decent publication rate. However I had also the idea that string theory was far of phenomenology, and I had not purchased too mcuh that topic.
F-theory minirevolution has changed that. I have read at last the two big pioneer papers of Vafa (arXiv:0802.3391v1 and arXiv:0806.0102v1), and almost completed the reading of the F-theory Guts cosmology (arXiv:0812.3155v1). Also I have made partial readings of some subsequent papers, and a few previous papers needed to understand the formalism developed.
Certainly are hard to understand papers. But once one gets familiar with them one sees what kind of physics is discussed. The first thing to say is one need to know the details of GUT's and symmetry (and supersymmetry) breaking. F-theory local models, with the right decoupling from gravity, can give an SU(5) model, without any exotics. They offer it's own way to break SU(5) into the MSSM, through an U(1) flux of hyperchrge, That mechanism avoids some of the problems presents in purely field theoretic models. In particular they can avoid problems with the observed lifetime of the proton. Ulterior papers get values in the CKM matrix that are good to get the observed asymetry oof baryons in universe. They offer ways to advoid the singlet-tripplet spliting problem of GUT's (That is, requiring the existence of Higgs doublets (1, 2)±1/2 leads necessarily also to color triplets. However, there exist rather uncomfortable lower bounds on the mass of these triplets). They offer a natural way to get small neutrino masses. In cosmology, trough a late decay of the saxion (whose lifetimem is predicted, that is, properly bounded, by the theory), they can avoid some of the problems that symmetry breaking bring to cosmology (the gravitino problem) and gives a righ way to obtain reheating after an inflactionary phase and some extra things that I haven't finished to read.
As you can see these models are quite near the cutting edge phenomenology. They offer solutions to problems not available by other approaches. And F-theory is not alone. Seemingly M-theory is going also into the local models + gravity decoupling business, see for example the paper Hitchin’s Equations and M-Theory Phenomenology by Tony Pantev and Martijn Wijnholt.
As I said I hadn't followed previously phenomenology with too much attention. But, in fact, more traditional approaches also had made some advances. For example this 2008 short review article of heterotic compactifications, From strings to the MSSM also cares about some of the previously mentioned aspects.
Another very recent paper, Towards Realistic String Vacua From Branes At Singularities, by Joseph P. Conlon, Anshuman Maharana, Fernando Quevedo, use the D-brane approach to phenomenology, not related to the gravity decoupling approach. They offer the bonus of moduli stabilization (something more habitual in cosmological models). In the abstract the conclude saying: "We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron’s CDF detector". Well, there some serious doubts about the real existence of that anomalies (see the tomasso dorigo´s blog, linked in this web site, and search for discussion of that topic).
Well, certainly there are a few bunch of models inspired by string theory, and not all of them (if any) can be truth at once. Also not all models make firm predictions. But the point is that they are actually reproducing the MSSM, GUT´s supersymmetric models, and mechanism to enhance the purely particle physics models. Also , in cosmology there are many different points where string is enhancing purely field theoretic models.
But, such as I see it, string theory is actually dictating the construction of (at least some of) the models that are going to be checked in the near future. Also one must not forget about the RS models, inspired by string theory, where one could get black holes in the LHC (that models possibly are not compatible with F-theory GUTs).
With all of this I think that string theory is doing exactly what one would expect from a traditional fundamental theory of physics such it has been made traditionally. Certainly I am talking about very, very, recent developments, most of them from this year and the previous one. But, anyway, it looks like if string theory is definitively "landing" into experimental physics, that is what it was expected from it. And, still, it is doing progress into clarifying it`s theoretical aspects, and the description of black holes (a topic not too easy to study in laboratory, except if LCH produce black holes, that is).
I am not at all a radical and I understand if some people wants to keep doing alternative approaches. The point of this post is to say that, as far as I see, the "not even wrong" criticism of string theory doesn't make too much sense nowadays.
And please, remember that I am not in a faculty position getting money from doing research in string theory. I have no economic, doctrinal or political reason to favour one theory or another. It is just that, according to what I know just now, string theory seems a perfectly good theory for doing high energy physics, and I have tried to explain why.
The post was a translation to Spanish of an article in new scientist about the good points of string theory. I had seen a discussion of that article in Lubos blog, concretely here.
Well, that article comes to say that string theory is nowadays a good theory because it´s math structure, through the AdS/CFT correspondence is useful in QCD and condensed matter physics. Well, I don't know too much about that applications but if the experts in that subjects say so is a good sign.
But, actually, I don't think that that image is quite right nowadays. Readers of this blog know that I have played attention to many alternative theories. Some of the proponents of that theories make claims against string theory. Others, who don't actually offer any theory, that is, Peter Woit, claims that string theory "makes no predictions". In his blog he usually bring attention mostly to the most speculative articles written by string theorists.
Well, I am following, as much as I can, the actual F-theory minirevolution. Doing so I have become very surprised, and impressed, by how close string theory has become of actual physics. Before going into it I must say that I somewhat understand the sceptics in string theory. If one reads the books on the subject one certainly gets the impression that actual predictions are far away. For example the 1999 (that is, not too old) book of Michio Kaku Introduction to superstrings and M-theory in its chapters about phenonenology show the results of heterotic compactifications. In that results the best one could get were the standard model plus some additional U(1) factors. Also it was stated that to achieve the right number of generations , given by n=1/2X(Cy), that is, one half of the Euler characteristic of the Calabi-Yau mainfold, was difficoult (if not almost impossible).
Other books, as Polchinsky´s two volumes book and the Clifford Jones "D-branes" don't say too much about realistic compactifications. There are good reasons for that. The books are mostly concerned about the D-brane revolutions and its consequences, the black hole entropy calculation and the AdS/CFT conjecture. The most recent book of Becker-Becker-Schwartz makes more in deep cover of compactifications. But , with a good criteria, somewhat cares more about technical issues such as the moduli space of the compactification, mirror symmetries among type II A and type II B, and flux compactifications, which are relevants for the very important issue of moduli stabilization and the KKLT like models (related to the landscape). And , of course, the all make introductions to dualities, M theory, and , to a least extent, F-theory.
In fact all that are important technical aspects, and it requires time to learn them (one must read some articles if he really wants to properly understand some aspects). But one gets the impression that everything is still to far from LHC phsyics and cosmology testable predictions. In fact there is a very recent book, by a Michel Dine which goes into phenomenology title "supersymmetry and superstrings". I must say that I find that book somewhat failed. It is to brief covering subjects that even with some previous knowledge are hard to appreciate properly.
Well, in definitive, a lot of text books and no a clear signal of actual testable physics. Certainly discouraging. Divulgative books are not too different. That, certainly, can explain why some people has the impression that string theory is far from it's objectives. Blogs from string theorists try to say, to whoever listen them, that string theory is "the only game in town". In fact there are not many blogs in string theory with a decent publication rate. However I had also the idea that string theory was far of phenomenology, and I had not purchased too mcuh that topic.
F-theory minirevolution has changed that. I have read at last the two big pioneer papers of Vafa (arXiv:0802.3391v1 and arXiv:0806.0102v1), and almost completed the reading of the F-theory Guts cosmology (arXiv:0812.3155v1). Also I have made partial readings of some subsequent papers, and a few previous papers needed to understand the formalism developed.
Certainly are hard to understand papers. But once one gets familiar with them one sees what kind of physics is discussed. The first thing to say is one need to know the details of GUT's and symmetry (and supersymmetry) breaking. F-theory local models, with the right decoupling from gravity, can give an SU(5) model, without any exotics. They offer it's own way to break SU(5) into the MSSM, through an U(1) flux of hyperchrge, That mechanism avoids some of the problems presents in purely field theoretic models. In particular they can avoid problems with the observed lifetime of the proton. Ulterior papers get values in the CKM matrix that are good to get the observed asymetry oof baryons in universe. They offer ways to advoid the singlet-tripplet spliting problem of GUT's (That is, requiring the existence of Higgs doublets (1, 2)±1/2 leads necessarily also to color triplets. However, there exist rather uncomfortable lower bounds on the mass of these triplets). They offer a natural way to get small neutrino masses. In cosmology, trough a late decay of the saxion (whose lifetimem is predicted, that is, properly bounded, by the theory), they can avoid some of the problems that symmetry breaking bring to cosmology (the gravitino problem) and gives a righ way to obtain reheating after an inflactionary phase and some extra things that I haven't finished to read.
As you can see these models are quite near the cutting edge phenomenology. They offer solutions to problems not available by other approaches. And F-theory is not alone. Seemingly M-theory is going also into the local models + gravity decoupling business, see for example the paper Hitchin’s Equations and M-Theory Phenomenology by Tony Pantev and Martijn Wijnholt.
As I said I hadn't followed previously phenomenology with too much attention. But, in fact, more traditional approaches also had made some advances. For example this 2008 short review article of heterotic compactifications, From strings to the MSSM also cares about some of the previously mentioned aspects.
Another very recent paper, Towards Realistic String Vacua From Branes At Singularities, by Joseph P. Conlon, Anshuman Maharana, Fernando Quevedo, use the D-brane approach to phenomenology, not related to the gravity decoupling approach. They offer the bonus of moduli stabilization (something more habitual in cosmological models). In the abstract the conclude saying: "We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron’s CDF detector". Well, there some serious doubts about the real existence of that anomalies (see the tomasso dorigo´s blog, linked in this web site, and search for discussion of that topic).
Well, certainly there are a few bunch of models inspired by string theory, and not all of them (if any) can be truth at once. Also not all models make firm predictions. But the point is that they are actually reproducing the MSSM, GUT´s supersymmetric models, and mechanism to enhance the purely particle physics models. Also , in cosmology there are many different points where string is enhancing purely field theoretic models.
But, such as I see it, string theory is actually dictating the construction of (at least some of) the models that are going to be checked in the near future. Also one must not forget about the RS models, inspired by string theory, where one could get black holes in the LHC (that models possibly are not compatible with F-theory GUTs).
With all of this I think that string theory is doing exactly what one would expect from a traditional fundamental theory of physics such it has been made traditionally. Certainly I am talking about very, very, recent developments, most of them from this year and the previous one. But, anyway, it looks like if string theory is definitively "landing" into experimental physics, that is what it was expected from it. And, still, it is doing progress into clarifying it`s theoretical aspects, and the description of black holes (a topic not too easy to study in laboratory, except if LCH produce black holes, that is).
I am not at all a radical and I understand if some people wants to keep doing alternative approaches. The point of this post is to say that, as far as I see, the "not even wrong" criticism of string theory doesn't make too much sense nowadays.
And please, remember that I am not in a faculty position getting money from doing research in string theory. I have no economic, doctrinal or political reason to favour one theory or another. It is just that, according to what I know just now, string theory seems a perfectly good theory for doing high energy physics, and I have tried to explain why.
Thursday, May 14, 2009
Prehistory of the F-theory GUTs (mini?)- revolution
After an intensive training in algebraic geometry and the reading of the use of type II-B/F-theory in cosmology (KKLT, moduli stabilization and all that) I tried to do a direct attack to the two papers that initiated the F-theory revolution.
I had read generic aspects of them in the Lubos and Distler's blogs (well, Distler is actually disappeared and only put an entry about the first paper, this). I also found useful an entry in U-duality blog linking a paper of Schwartzabout the status of superstring theory, this entry
Well, my attack flailed miserably. I remotely understood some of the statements but I didn´t understand where they come from. I needed to go to the bibliography of the Vafa et all papers. I also have found clarifying some hints in follow up papers.
The first thing that I needed to understand properly is what a local model is. The proposal of local models seems to be born in a paper by (mostly) Spanish string theorist´s: G. Aldazabal1, L. E. Ib´a˜nez2, F. Quevedo3 and A. M. Uranga in the paper D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model
The idea is to do instead of a top-down approach, that is, choose a compactification, study the resulting physic and see how well it matches the MSSM (minimal supersymmetric standard model) or something resembling the known physic one does a bottom up approach. It consists of two steps (I cite form the paper):
i) Look for local configurations of D-branes with worldvolume theories resembling
the SM as much as possible. In particular we should search for a gauge group SU(3) ×
SU(2) × U(1) but also for the presence of three chiral quark-lepton generations. Asking
also for D = 4 N = 1 unbroken supersymmetry may be optional, depending on what
our assumptions about what solves the hierarchy problem are. At this level the theory
needs no compactification and the D-branes may be embedded in the full 10-dimensional
Minkowski space. On the other hand, gravity still remains ten-dimensional, and hence
this cannot be the whole story.
ii) The above local D-brane configuration may in general be part of a larger global
model. In particular, if the six transverse dimensions are now compactified, one can in
general obtain appropriate four-dimensional gravity with Planck mass proportional to the
compactification radii.
In that paper the fields come form D-bran physics, i.e. open strings ending on the branes. They consider the branes suited at singularities of an orbifold. In F-Theory (and also M-theory) that approach takes a much more difficult form, but the idea is the same.
By the way, the idea of local models has had some development outside of the F-theory revolution, see for example Building the Standard Model on a D3-brane, by the Verlinde brothers. In general that attempts were influenced by the paradigm of D-brane intersections (of which I don´t know too much neither).
Almost at the same time that the now famous Vafa papers it appeared in arxiv another paper on model building with F-theory by Ron Donagi and Martijn Wijnholt (arXiv:0802.2969v2). I find that paper very illuminating. It explains in a very accessible way many facts of F-theory. For example the difference of the 7-brane of F-theory, which is not necessarily an D-brane but instead is a brane where a (p,q) string can end. It also clarifies the geometric idea behind the local model approach and gives intuitions on how gauge matter can appears, based in considerations of the supersymetry limit of F-theory.
I still haven't read all the paper. But in some point it talks about some of the other hard to follow questions of the F-theory revolution, the subject of ADE groups and it's relation to algebraic geometry and, in particular, the Kodaira classification of singularities.
That topic is covered in some early (mid nineties) papers of Vafa, for example Geometric Singularities and Enhanced Gauge Symmetries or Matter From Geometry
I am still trying to catch many aspects of how that works, but I believe that the essence of the argument is that F-theory and M-theory are related by dualities. Compactifiying F-theory in K3 surfaces (complex two dimensional Calabi-Yaus) is equivalent to compactify M-theory in a torus. The spectra of M-theory is easy to obtain and, by duality, one gets an idea of the particle spectra in F-theory and how it relates to the structure of the singularities. actually it is more complicated that that, and one must see how the idea holds in realistic compactifications. By the way, that work was previous to the local model engineering approach.
In this approach of F-theory the local model idea morphs into what is known as gravity decoupling. It is perfectly explained in the U-duality blog entry whcich I cite:
The criterion is that it should be possible to make the dimensions transverse to the 4-cycles wrapped by the 7-branes arbitrarily large. Equivalently, it should be possible to contract the 4-cycles to points while holding the six-dimensional volume fixed. Such contractible 4-cycles must be positive curvature Kahler manifolds. These are fully classified and are given by manifolds called del Pezzo manifolds (or del Pezzo surfaces), which are denoted dP_n. The integer n takes the values 0 ≤ n ≤ 8.9 The del Pezzos have a close relationship with the exceptional Lie algebras E_n. The basic idea is that they contain 2-cycles whose intersections are characterized by the E_n Dynkin diagram. By this type of F-theory construction, one can construct an SU(5) or SO(10) SUSY-GUT model. Constructions that involve 7-branes of various types are much more subtle – and also more interesting than ones that only involve D7-branes. D7-branes are mutually local. A stack of N of them gives U(N) gauge symmetry. Matter fields at intersections (due to stretched open strings) are bifundamental. However, different kinds of 7-branes are mutually nonlocal. As a result, there are stacks (corresponding to the ADE classification of singularities) that can give U(N), SO(2N) or even E_N gauge symmetry."
Well, this is just the beginning of the history. One must consider how the GUT groups are broken, this is achieved by means of hypercharge U(1) fluxes. I still must understand many points so I will stop here before misguiding to the possible readers.
I am finding very usefull this papers: F-theory Compactifications for Supersymmetric GUTs by Joseph Marsano, Natalia Saulina and Sakura Sch¨afer-Nameki and E ffective Field Theories for Local Models in F-Theory and M-Theory by Jacob L. Bourjaily.
This last one explains that, actually, the technology of the F-theory revolution also applies to M-theory. In fact both theories seem to have shared part of the development as is seem in the paper Chiral Fermions from Manifolds Of G2 Holonomy by Bobby Acharya and Edward Witten.
By the way, in the improbable case the reader wouldn't know what Vafa papers I am talking about here are the links: First paper and second paper
When I would gain a better understanding of the subject I'll try to do more posts on the subject, but certainly it would a good idea for my readers to see the Lubos blog entries on the same subject (and the Distler ones if he returns to the blogosphere). Well, surely there are more people out there who also could do a fine work bloging about those topics, certainly better than what can be reasonably expected form me .
By the way, a last note. This works are getting string theory very, very near of the phenomenology of LHC particle physics and cosmology testable effects. In fact it gets many pieces of actual physic by separate. Seemingly it "only" remains to join them. For example it must be addressed in deep the relevance of gin from local to global and the role that moduli stabilization plays there. Some work is on the way, but I will not give the links now. After all I wouldn´t like to fall in the category of "linker not thinker" ;-).
I had read generic aspects of them in the Lubos and Distler's blogs (well, Distler is actually disappeared and only put an entry about the first paper, this). I also found useful an entry in U-duality blog linking a paper of Schwartzabout the status of superstring theory, this entry
Well, my attack flailed miserably. I remotely understood some of the statements but I didn´t understand where they come from. I needed to go to the bibliography of the Vafa et all papers. I also have found clarifying some hints in follow up papers.
The first thing that I needed to understand properly is what a local model is. The proposal of local models seems to be born in a paper by (mostly) Spanish string theorist´s: G. Aldazabal1, L. E. Ib´a˜nez2, F. Quevedo3 and A. M. Uranga in the paper D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model
The idea is to do instead of a top-down approach, that is, choose a compactification, study the resulting physic and see how well it matches the MSSM (minimal supersymmetric standard model) or something resembling the known physic one does a bottom up approach. It consists of two steps (I cite form the paper):
i) Look for local configurations of D-branes with worldvolume theories resembling
the SM as much as possible. In particular we should search for a gauge group SU(3) ×
SU(2) × U(1) but also for the presence of three chiral quark-lepton generations. Asking
also for D = 4 N = 1 unbroken supersymmetry may be optional, depending on what
our assumptions about what solves the hierarchy problem are. At this level the theory
needs no compactification and the D-branes may be embedded in the full 10-dimensional
Minkowski space. On the other hand, gravity still remains ten-dimensional, and hence
this cannot be the whole story.
ii) The above local D-brane configuration may in general be part of a larger global
model. In particular, if the six transverse dimensions are now compactified, one can in
general obtain appropriate four-dimensional gravity with Planck mass proportional to the
compactification radii.
In that paper the fields come form D-bran physics, i.e. open strings ending on the branes. They consider the branes suited at singularities of an orbifold. In F-Theory (and also M-theory) that approach takes a much more difficult form, but the idea is the same.
By the way, the idea of local models has had some development outside of the F-theory revolution, see for example Building the Standard Model on a D3-brane, by the Verlinde brothers. In general that attempts were influenced by the paradigm of D-brane intersections (of which I don´t know too much neither).
Almost at the same time that the now famous Vafa papers it appeared in arxiv another paper on model building with F-theory by Ron Donagi and Martijn Wijnholt (arXiv:0802.2969v2). I find that paper very illuminating. It explains in a very accessible way many facts of F-theory. For example the difference of the 7-brane of F-theory, which is not necessarily an D-brane but instead is a brane where a (p,q) string can end. It also clarifies the geometric idea behind the local model approach and gives intuitions on how gauge matter can appears, based in considerations of the supersymetry limit of F-theory.
I still haven't read all the paper. But in some point it talks about some of the other hard to follow questions of the F-theory revolution, the subject of ADE groups and it's relation to algebraic geometry and, in particular, the Kodaira classification of singularities.
That topic is covered in some early (mid nineties) papers of Vafa, for example Geometric Singularities and Enhanced Gauge Symmetries or Matter From Geometry
I am still trying to catch many aspects of how that works, but I believe that the essence of the argument is that F-theory and M-theory are related by dualities. Compactifiying F-theory in K3 surfaces (complex two dimensional Calabi-Yaus) is equivalent to compactify M-theory in a torus. The spectra of M-theory is easy to obtain and, by duality, one gets an idea of the particle spectra in F-theory and how it relates to the structure of the singularities. actually it is more complicated that that, and one must see how the idea holds in realistic compactifications. By the way, that work was previous to the local model engineering approach.
In this approach of F-theory the local model idea morphs into what is known as gravity decoupling. It is perfectly explained in the U-duality blog entry whcich I cite:
The criterion is that it should be possible to make the dimensions transverse to the 4-cycles wrapped by the 7-branes arbitrarily large. Equivalently, it should be possible to contract the 4-cycles to points while holding the six-dimensional volume fixed. Such contractible 4-cycles must be positive curvature Kahler manifolds. These are fully classified and are given by manifolds called del Pezzo manifolds (or del Pezzo surfaces), which are denoted dP_n. The integer n takes the values 0 ≤ n ≤ 8.9 The del Pezzos have a close relationship with the exceptional Lie algebras E_n. The basic idea is that they contain 2-cycles whose intersections are characterized by the E_n Dynkin diagram. By this type of F-theory construction, one can construct an SU(5) or SO(10) SUSY-GUT model. Constructions that involve 7-branes of various types are much more subtle – and also more interesting than ones that only involve D7-branes. D7-branes are mutually local. A stack of N of them gives U(N) gauge symmetry. Matter fields at intersections (due to stretched open strings) are bifundamental. However, different kinds of 7-branes are mutually nonlocal. As a result, there are stacks (corresponding to the ADE classification of singularities) that can give U(N), SO(2N) or even E_N gauge symmetry."
Well, this is just the beginning of the history. One must consider how the GUT groups are broken, this is achieved by means of hypercharge U(1) fluxes. I still must understand many points so I will stop here before misguiding to the possible readers.
I am finding very usefull this papers: F-theory Compactifications for Supersymmetric GUTs by Joseph Marsano, Natalia Saulina and Sakura Sch¨afer-Nameki and E ffective Field Theories for Local Models in F-Theory and M-Theory by Jacob L. Bourjaily.
This last one explains that, actually, the technology of the F-theory revolution also applies to M-theory. In fact both theories seem to have shared part of the development as is seem in the paper Chiral Fermions from Manifolds Of G2 Holonomy by Bobby Acharya and Edward Witten.
By the way, in the improbable case the reader wouldn't know what Vafa papers I am talking about here are the links: First paper and second paper
When I would gain a better understanding of the subject I'll try to do more posts on the subject, but certainly it would a good idea for my readers to see the Lubos blog entries on the same subject (and the Distler ones if he returns to the blogosphere). Well, surely there are more people out there who also could do a fine work bloging about those topics, certainly better than what can be reasonably expected form me .
By the way, a last note. This works are getting string theory very, very near of the phenomenology of LHC particle physics and cosmology testable effects. In fact it gets many pieces of actual physic by separate. Seemingly it "only" remains to join them. For example it must be addressed in deep the relevance of gin from local to global and the role that moduli stabilization plays there. Some work is on the way, but I will not give the links now. After all I wouldn´t like to fall in the category of "linker not thinker" ;-).
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