I had said it before, but a new article, well, in fact two of them, almost consecutives, in arxiv, commented in the arxiv blog, brings again alive the question.

My point was to state that although cosmology is a legitimate topic, and that it has seen a fructiferous interplay with particle physic(in, for example, the BBN-big bang nucleosynthesis) cosmological observations are subject to many uncertainties. In my opinion that implies that one shouldn't sacrify the coherence and "physic common sense" of a theory it if not match some particular cosmological observation.

In particular I find that the problem of the cosmological constant is not enough reason to go into the landscape/anthropic scenery.

In the article Giant Lens May Be Distorting Echo of the Big Bang, based in the arsiv paper A Heliosheath Model for the Origin of the CMB Quadrupole Moment is stated that the analysis of the data send by the sputnik satellites when the left the solar system reveals that possibly the observed anisotropies in the CMB observed by COBE and WMAP could have an astrophysical origin, in the out shells of the solar system, and they don´t reflect a real cosmological anisotropy. that is certainly very important because the recently launched PLANCK and HERSCHELL satellites are supposed to make a better measure of that polarizations. Supossedly the sensitivity of that measures would allow to tests some models of inflation. But if the measured quantities are of astrophysical origin the utility of the whole busines would change radically.

Today other article claim to have a model for the accelerated cosmological expansion baed on five foreces actin in long ranges (but in not shor ones). Certainly it is not the first, and it will not be the last, article who proposes an alternative to the cosmological constant. For example, as far as I know models based in "quintaessence" are not ruled out. I personally find unnecessary to go into the landscape when it is reasonable to expect better explanations for the observed expansion of the universe. And, well, as the previous article clearly shows it is a good idea to be cautious about the accuracy and veracity of cosmological data.

## Monday, May 25, 2009

## 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 Effective 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 Effective 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" ;-).

Etiquetas:
F-theory,
string theory

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