The last Friday there was a very interesting paper in arxiv. I am really busy those days (and it will be so until around the 15 of September)so I couldn't still read ot completely. Still I think that I must leave notice of it here.

The paper in question is title like the post entry, Geometric Models of Matter. It has three authors: Michael Atiyah, Nicholas S. Manton, Bernd J. Schroers. Among them the best known one is, of course, sir Michaell Atiyhay, a very well known field medallist in mathemathics.

The abstract of the paper reads:

Inspired by soliton models, we propose a description of static particles in terms of Riemannian 4-manifolds with self-dual Weyl tensor. For electrically charged particles, the 4-manifolds are non-compact and asymptotically fibred by circles over physical 3-space. This is akin to the Kaluza-Klein description of electromagnetism, except that we exchange the roles of magnetic and electric fields, and only assume the bundle structure asymptotically, away from the core of the particle in question. We identify the Chern class of the circle bundle at infinity with minus the electric charge and the signature of the 4-manifold with the baryon number. Electrically neutral particles are described by compact 4-manifolds. We illustrate our approach by studying the Taub-NUT manifold as a model for the electron, the Atiyah-Hitchin manifold as a model for the proton, CP^2 with the Fubini-Study metric as a model for the neutron, and S^4 with its standard metric as a model for the neutrino.

Ok, as I said I still didn't read the full article so I can't say many detaills. But the idea seems simple. They are inspired in the Skyrme modell. There there is a group-valued field from :$$mathbb{R}^3$$

$$U:mathbb{R}^3 \rightarrow G$$.

where the lie group is usually SU(2). In that construction specific characteristics of the proton and neutron (baryon number and so on)are associated to topological constructions, that aare, automatically, conserved quantities.

In the paper they generalize the idea in order to construct another particles, for example the electron. They must choose different kinds of manifolds, and maps. Also they use different topological invariants and so on.

But the idea is that they try to describe matter, and it's associated charges, in basic to purely geometric/topologyc constructions. Of course we are talking about different constructions that the one's involved in gauge theories. The proposal of Atiyah and all somewhat replace the need of an ordinary QFT to begin with. IF I have understood right they only have by now an static construction, that is, they don't have a way to give a dynamics to their theory. That means that it remains a lot of work to be done before they get something remotely similar to the actual world.

But, still, it is a beautiful (at least mathematically) idea. For sure Einstein would have loved it. Let's remember that in GR the space-time has a geometric nature while matter has a non-geometric one. In that sense it is an inelegant theory. If this construction works we would have a fully geometric description of the universe. If that works the immediate answer would be: the resulting theory would be equivalent to ordinary QFT in curved (well, maybe we would first ask for flat space-time9 space time for usual situations? would it give some advantage, other than aesthetic? could it be promoted to a quantum gravity?

Whatever the answer to these questions could be I think that it looks like a theory that deserves some further development. Even if it fails like a viable physical theory it could be a source of new ideas for existing ones.

## Monday, August 29, 2011

## Monday, May 30, 2011

### Great day in arxiv

Today there are in arxiv two articles that look really great.

The firs (in the order that arxiv gives to them) is from Samir D. Mathur: Effective information loss outside the horizon.

It argues that there is no loss of information inside a black hole because he information simply doesn't go inside the black hole. The abstract explains it more carefully:

If a system falls through a black hole horizon, then its information is lost to an observer at infinity. But we argue that the {\it accessible} information is lost {\it before} the horizon is crossed. The temperature of the hole limits information carrying signals from a system that has fallen too close to the horizon. Extremal holes have T=0, but there is a minimum energy required to emit a quantum in the short proper time left before the horizon is crossed. If we attempt to bring the system back to infinity for observation, then acceleration radiation destroys the information. All three considerations give a critical distance from the horizon $d\sim \sqrt{r_H\over \Delta E}$, where $r_H$ is the horizon radius and $\Delta E$ is the energy scale characterizing the system. For systems in string theory where we pack information as densely as possible, this acceleration constraint is found to have a geometric interpretation. These estimates suggest that in theories of gravity we should measure information not as a quantity contained inside a given system, but in terms of how much of that information can be reliably accessed by another observer.

The other article is written by Maldacena: Einstein Gravity from Conformal Gravity.

The abstract is:

We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation. In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, $|\Psi [ g ]|^2$, for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.">We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation.

In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, $|\Psi [ g ]|^2$, for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.

Unfortunately until the next Friday I am going to be very busy and I badly will have time to read them carefully those days so I can't say too much more about them. I suppose that (at least) Lubos will talk about them so I will read its report before I can read them myself. I write this entry partially to recommend the articles to however could be interested and also to keep a link to them so I could later have a quick access to them from wherever I want.

Update: Well, at last I had no patient and read the first article (after all is a brief one, only 7 pages). I have a mixed filling about it. The author computes a few things related to the fall of a body towards an event horizon. Firstly he does for an Schwarschild one.

There he considers two cases. The first in the free fall. In that case the last light (containing the info about the object) is emitted, because of the red-shift at a frequency bellow the Hawking temperature and so it can't be differentiated from this and he concludes that we actually don't have the information about that object.

The second case is when an observer at infinity holds the infalling object until the last time. In that case it is the unrhu radiation associated to the acceleration of an object at rest respect to a gravitational field which is responsible for a dissipation of the information of the object when it finally is released and cross the horizont.

Later he calculates similar things for a Reissner-Nordstöm like black hole and he finds that somewhat different mechanism operate in order to get similar qualitative and quantitative results.

In the last part he does calculations using string theory and the fuzzball paradigm for black holes (where the notion of event horizon is replaced by an stringy construction). Still he finds equivalent results.

Certainly the fact that many different calculations lead to a similar result is appealing. But still I don't see clear the whole subject. I think that at best he would be saying that the lost of information happens before the horizon (or its fuzzball "equivalent") so the problem of lost of unitarity remains (and even we could say that is getting worst because it happens in a region causally connected with the outsider observer). But the whole thing is that one could think that a priory we could think that if the outside of the black hole is clean of other infalling matter (other that the actual object under study) we could argue that if we know the state of the object at infinity we can apply the laws of quantum mechanics to know t's state when it is falling (eve it we can't actually do a measure to be sure that nothing has perturbed our object). That contrast the case of the object that falls behind the horizon when we have no idea of which it's final state would be because we don't know the laws of quantum gravity near the singularity. Well, I am ware that this last objection is somewhat wrong because the key point of the lost of information is the horizon and not the singularity but I have no more time just now to see what point I am missing. I'll realize it for sure later, but I don't promise to write it here soon. But keep calm, for sure Lubos will write about it sooner or later and will clarify the relevant points ;).

The firs (in the order that arxiv gives to them) is from Samir D. Mathur: Effective information loss outside the horizon.

It argues that there is no loss of information inside a black hole because he information simply doesn't go inside the black hole. The abstract explains it more carefully:

If a system falls through a black hole horizon, then its information is lost to an observer at infinity. But we argue that the {\it accessible} information is lost {\it before} the horizon is crossed. The temperature of the hole limits information carrying signals from a system that has fallen too close to the horizon. Extremal holes have T=0, but there is a minimum energy required to emit a quantum in the short proper time left before the horizon is crossed. If we attempt to bring the system back to infinity for observation, then acceleration radiation destroys the information. All three considerations give a critical distance from the horizon $d\sim \sqrt{r_H\over \Delta E}$, where $r_H$ is the horizon radius and $\Delta E$ is the energy scale characterizing the system. For systems in string theory where we pack information as densely as possible, this acceleration constraint is found to have a geometric interpretation. These estimates suggest that in theories of gravity we should measure information not as a quantity contained inside a given system, but in terms of how much of that information can be reliably accessed by another observer.

The other article is written by Maldacena: Einstein Gravity from Conformal Gravity.

The abstract is:

We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation. In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, $|\Psi [ g ]|^2$, for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.">We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation.

In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, $|\Psi [ g ]|^2$, for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.

Unfortunately until the next Friday I am going to be very busy and I badly will have time to read them carefully those days so I can't say too much more about them. I suppose that (at least) Lubos will talk about them so I will read its report before I can read them myself. I write this entry partially to recommend the articles to however could be interested and also to keep a link to them so I could later have a quick access to them from wherever I want.

Update: Well, at last I had no patient and read the first article (after all is a brief one, only 7 pages). I have a mixed filling about it. The author computes a few things related to the fall of a body towards an event horizon. Firstly he does for an Schwarschild one.

There he considers two cases. The first in the free fall. In that case the last light (containing the info about the object) is emitted, because of the red-shift at a frequency bellow the Hawking temperature and so it can't be differentiated from this and he concludes that we actually don't have the information about that object.

The second case is when an observer at infinity holds the infalling object until the last time. In that case it is the unrhu radiation associated to the acceleration of an object at rest respect to a gravitational field which is responsible for a dissipation of the information of the object when it finally is released and cross the horizont.

Later he calculates similar things for a Reissner-Nordstöm like black hole and he finds that somewhat different mechanism operate in order to get similar qualitative and quantitative results.

In the last part he does calculations using string theory and the fuzzball paradigm for black holes (where the notion of event horizon is replaced by an stringy construction). Still he finds equivalent results.

Certainly the fact that many different calculations lead to a similar result is appealing. But still I don't see clear the whole subject. I think that at best he would be saying that the lost of information happens before the horizon (or its fuzzball "equivalent") so the problem of lost of unitarity remains (and even we could say that is getting worst because it happens in a region causally connected with the outsider observer). But the whole thing is that one could think that a priory we could think that if the outside of the black hole is clean of other infalling matter (other that the actual object under study) we could argue that if we know the state of the object at infinity we can apply the laws of quantum mechanics to know t's state when it is falling (eve it we can't actually do a measure to be sure that nothing has perturbed our object). That contrast the case of the object that falls behind the horizon when we have no idea of which it's final state would be because we don't know the laws of quantum gravity near the singularity. Well, I am ware that this last objection is somewhat wrong because the key point of the lost of information is the horizon and not the singularity but I have no more time just now to see what point I am missing. I'll realize it for sure later, but I don't promise to write it here soon. But keep calm, for sure Lubos will write about it sooner or later and will clarify the relevant points ;).

Etiquetas:
black holes,
string theory

## Tuesday, April 19, 2011

### Can we see inside black holes?

The last week there was an article that was commented in the arxiv blog: Planets Could Orbit Singularities Inside Black Holes.

The blog entry discuses this article: Is there life inside black holes?.

The article is a pure classical relativity article. It study the possibility of stable orbits for planets inside a black hole, in particular in a Kerr-Newman black hole, that is, a rotting charged black hole. The classical geometry of a Kerr-Newman black hole is described by it's Penrose diagram:

The essential aspect of the K-N black holes for the work of that people is the presence of the inner horizon (a Cauchy horizon). In a non rotating black hole, described by the Schwarschild metric, once he cross the event horizon the radial coordinate changes it sign acquiring a time sign. That means that one must go in the direction of decreasing radius until one finds the central point-like singularity. A common interpretation of that geometry is to say that inside the black hole the space itself is falling toward the centre at the speed of light and it drags averything with it.

In the K-N case things are somewhat richer. In addition to the outer event horizon there is an inner cauchy horizon. When the black holes spins faster and faster (or when the charge of the black hole increases) both horizons get nearest and nearest until, ultimately, they would converge and it would become an extreme black hole.Beyond that one would have a naked singularity but it is thought that such a possibility should be ruled out.

well, as a I said te key point was the cuchy horizon. AS you can read in the linked wikipedia article a Cauchy Horizon is a boundary for the validity of a well posed Cauchy problem in partial differential equations. It can be shown that light (or whatever wave) crossing the horizon gets an infinite blue-shift. That means that it's energy-momentum tensor diverges. The implication of it would be that the back-reaction would destroy the Cauchy horizon once a particle cross it. Still one could get an stable Cauchy horizon if one throws in it exotic matter violating the AWEC (average weak energy condition) well known for people working in wormholes.

The reason why the cauchy horizon is important is because once it is crossed the radial coordinate becomes once again space like. That opens the possibility of the existence of stable orbits inside the black hole. In previous articles, cited by the author, it was shown the existence of that orbits for Reisner-Nordstöm (charged) and Kerr (rotating) black holes. The present article generalizes the results to the general case. In the article considerations are hold about the tidal forces, sizes, radiation rates and they conclude that in a galaxy centre sized black hole a planet could do an stable orbit around the singularity and hold life.

Well, this is the content of the article. As I have explained it is worked in the ansatz of the validity of classical relativity inside a black hole. Also it depends strongly in the stability of the cauchy horizon that can't be got without exotic matter. Note: the author doesn't mention that point about exotic matter although he is aware of the fact that cauchy horizons are not stable. Without exotic matter the whole paper is of a purely academic interest even if one accepts that classical general relativity is accurate to describe black holes inners.

Of course there are a lot of people who don't like classical GR for doing so. In string theory there are many alternative descriptions. On one side one has the correspondence principle of black holes (due to t' hooft and Suskind) that says that an observer falling into a black hole will not be able to notice when he has crossed the even horizon. That means that the physic he sees is must be equal that the physics seen by an outside observer. The reason of the introduction of that principle is the intent of saving unitarity in the presence of Hawking radiation. The actual reasoning is made not classically but for the Hilbert space of a quantum theory as seen but inner and outer observers.

Another string theory inspired viewpoint is described in a classical article by Maldacena: D-brane Approach to Black Hole Quantum Mechanics . In the last part of that article, after calculating the Beckenstein-Hawking entropy, Maldacena Suggest a view where black holes inners and Hawking radiation is described in terms of D-branes. I am not aware if that suggestion has been further developed. I have made a partial search for "hawking radiation in string theory" but I haven't found too much. In fact, beyond that Maldacena article, I found only an approach written some years before using a very aproximative description.

Another paradigm for black hole inners in the string literature would be the fuzzball approach of Mahupart (or maybe Mithur I am not sure at this point and have not time to do a search just now).

Well, that variety of viewpoints, not very compatible among them, for the black hole inner is disappointing. Even in the simpler case of the general relativity viewpoint is disappointing the possibility of the existence of stable structures (maybe planets of an advanced alien civilization, maybe a much more prosaic rings of dust) existing inside the black hole hidden for us from the event horizon.

But, wait! The title of the post wonders about the possibility of seeing inside the black hole. Of course classically it is impossible because of the very meaning of "event horizon". But when quantum mechanics enter the game thing could change. Of course the key would be Hawking radiation. The semiclassical theory says that the radiation must be purely thermodynamic so we can't get any info from it. But if unitarity is conserved the Hawking radiation can't be purely thermodynamic and it must have some structure that stores all the structure of the matter that formed the black hole and that has fallen inside it after it's formation. Possibly it will also have some information about the inner structure of the black hole. Obviously to get that info is very difficult in practice. The usual analogy is to say that one could reconstruct, in principle, the form of a living object from the ashes that are produced when it is burn.

But if we are a little least ambitious maybe we could actually get some partial information. Maybe we could design some easy mental experiment in which throwing into the black hole some specific kind of matter in some specific way we could analyse the Hawking radiation related to it to get some information of the inside of the horizon. That would actually be very cool because it would give an experimental way to distinguish the competing descriptions of the black hole inner.

Of course I actually don't know the details of how this could be done (only a very vague ideas that probably will not work). But maybe something on this purpose is already made and a kind reader would give me the references ;).

The blog entry discuses this article: Is there life inside black holes?.

The article is a pure classical relativity article. It study the possibility of stable orbits for planets inside a black hole, in particular in a Kerr-Newman black hole, that is, a rotting charged black hole. The classical geometry of a Kerr-Newman black hole is described by it's Penrose diagram:

The essential aspect of the K-N black holes for the work of that people is the presence of the inner horizon (a Cauchy horizon). In a non rotating black hole, described by the Schwarschild metric, once he cross the event horizon the radial coordinate changes it sign acquiring a time sign. That means that one must go in the direction of decreasing radius until one finds the central point-like singularity. A common interpretation of that geometry is to say that inside the black hole the space itself is falling toward the centre at the speed of light and it drags averything with it.

In the K-N case things are somewhat richer. In addition to the outer event horizon there is an inner cauchy horizon. When the black holes spins faster and faster (or when the charge of the black hole increases) both horizons get nearest and nearest until, ultimately, they would converge and it would become an extreme black hole.Beyond that one would have a naked singularity but it is thought that such a possibility should be ruled out.

well, as a I said te key point was the cuchy horizon. AS you can read in the linked wikipedia article a Cauchy Horizon is a boundary for the validity of a well posed Cauchy problem in partial differential equations. It can be shown that light (or whatever wave) crossing the horizon gets an infinite blue-shift. That means that it's energy-momentum tensor diverges. The implication of it would be that the back-reaction would destroy the Cauchy horizon once a particle cross it. Still one could get an stable Cauchy horizon if one throws in it exotic matter violating the AWEC (average weak energy condition) well known for people working in wormholes.

The reason why the cauchy horizon is important is because once it is crossed the radial coordinate becomes once again space like. That opens the possibility of the existence of stable orbits inside the black hole. In previous articles, cited by the author, it was shown the existence of that orbits for Reisner-Nordstöm (charged) and Kerr (rotating) black holes. The present article generalizes the results to the general case. In the article considerations are hold about the tidal forces, sizes, radiation rates and they conclude that in a galaxy centre sized black hole a planet could do an stable orbit around the singularity and hold life.

Well, this is the content of the article. As I have explained it is worked in the ansatz of the validity of classical relativity inside a black hole. Also it depends strongly in the stability of the cauchy horizon that can't be got without exotic matter. Note: the author doesn't mention that point about exotic matter although he is aware of the fact that cauchy horizons are not stable. Without exotic matter the whole paper is of a purely academic interest even if one accepts that classical general relativity is accurate to describe black holes inners.

Of course there are a lot of people who don't like classical GR for doing so. In string theory there are many alternative descriptions. On one side one has the correspondence principle of black holes (due to t' hooft and Suskind) that says that an observer falling into a black hole will not be able to notice when he has crossed the even horizon. That means that the physic he sees is must be equal that the physics seen by an outside observer. The reason of the introduction of that principle is the intent of saving unitarity in the presence of Hawking radiation. The actual reasoning is made not classically but for the Hilbert space of a quantum theory as seen but inner and outer observers.

Another string theory inspired viewpoint is described in a classical article by Maldacena: D-brane Approach to Black Hole Quantum Mechanics . In the last part of that article, after calculating the Beckenstein-Hawking entropy, Maldacena Suggest a view where black holes inners and Hawking radiation is described in terms of D-branes. I am not aware if that suggestion has been further developed. I have made a partial search for "hawking radiation in string theory" but I haven't found too much. In fact, beyond that Maldacena article, I found only an approach written some years before using a very aproximative description.

Another paradigm for black hole inners in the string literature would be the fuzzball approach of Mahupart (or maybe Mithur I am not sure at this point and have not time to do a search just now).

Well, that variety of viewpoints, not very compatible among them, for the black hole inner is disappointing. Even in the simpler case of the general relativity viewpoint is disappointing the possibility of the existence of stable structures (maybe planets of an advanced alien civilization, maybe a much more prosaic rings of dust) existing inside the black hole hidden for us from the event horizon.

But, wait! The title of the post wonders about the possibility of seeing inside the black hole. Of course classically it is impossible because of the very meaning of "event horizon". But when quantum mechanics enter the game thing could change. Of course the key would be Hawking radiation. The semiclassical theory says that the radiation must be purely thermodynamic so we can't get any info from it. But if unitarity is conserved the Hawking radiation can't be purely thermodynamic and it must have some structure that stores all the structure of the matter that formed the black hole and that has fallen inside it after it's formation. Possibly it will also have some information about the inner structure of the black hole. Obviously to get that info is very difficult in practice. The usual analogy is to say that one could reconstruct, in principle, the form of a living object from the ashes that are produced when it is burn.

But if we are a little least ambitious maybe we could actually get some partial information. Maybe we could design some easy mental experiment in which throwing into the black hole some specific kind of matter in some specific way we could analyse the Hawking radiation related to it to get some information of the inside of the horizon. That would actually be very cool because it would give an experimental way to distinguish the competing descriptions of the black hole inner.

Of course I actually don't know the details of how this could be done (only a very vague ideas that probably will not work). But maybe something on this purpose is already made and a kind reader would give me the references ;).

Etiquetas:
black holes,
string theory

## Thursday, February 17, 2011

### String theory in exotic R^4

Today in arxiv there is a very curious article:Quantum D-branes and exotic smooth R^4 written by Torsten Asselmeyer-Maluga, Jerzy Krol.

The article is actually the second part of a previous one: Exotic smooth R^4 and certain configurations of NS and D branes in string theory.

The abstract of the first (in date order) article reads:

In this paper we show that in some important cases 4-dimensional data can be extracted from superstring theory such that a) the data are 4 Euclidean geometries embedded in standard $\mathbb{R}^{4}$, b) these data depend on NS and D brane charges of some string backgrounds, c) it is of potential relevance to 4-dimensional physics, d) the compactification and stabilization techniques are not in use, but rather are replaced. We analyze certain configurations of NS and D-branes in the context of $SU(2)$ WZW model and find the correlations with different exotic smoothings of $\mathbb{R}^{4}$. First, the dynamics of D-branes in $SU(2)$ WZW model at finite $k$, i.e. the charges of the branes, refers to the exoticness of ambient $\mathbb{R}^{4}$. Next, the correspondence between exotic smoothness on 4-space, transversal to the world volume of NS5 branes in IIA type, and the number of these NS5 branes follows. Finally, the translation of 10 dimensional string backgrounds to 4 Euclidean spaces embedded as open subsets in the standard $\mathbb{R}^{4}$ is achieved.

I still haven't had time to read the full article, but it looks quite interesting, and beautifully, specially from the perspective of someone whose favourite area of maths is topology. The idea is to see if someone can make string theory in a background of R^4 with a different differential structure than the usual one. One of the most amazing discoveries of differential topology was that there were different differential structures for R^4 than the usual one. That means that although like a topological manifold R^4 is unique there are different differentiable manifolds that are compatible with it's topological structure. An explicit characterization of that exotic structures in terms of coordinate is difficult and their existence is proved by means of topological techniques. In the paper it is made use of h-cobordism.

Later he begins the string theoretical construction, using SU(2) WZW (wess-zumino-witten= CFT's, NS 5 branes, D branes, etc. AS I still haven't read the article carefully, nor the continuation of it (the today's arxiv article ) wouldn't give more details. Only to say that it looks like a very intriguing area of research.

Also today in arxiv there is a very interesting, but much more conventional article of Miche Dine: Supersymmetry from the Top Down whose abstract is:

If supersymmetry turns out to be a symmetry of nature at low energies, the first order of business to measure the soft breaking parameters. But one will also want to understand the symmetry, and its breaking, more microscopically. Two aspects of this problem constitute the focus of these lectures. First, what sorts of dynamics might account for supersymmetry breaking, and its manifestation at low energies. Second, how might these features fit into string theory (or whatever might be the underlying theory in the ultraviolet). The last few years have seen a much improved understanding of the first set of questions, and at least a possible pathway to address the second.">If supersymmetry turns out to be a symmetry of nature at low energies, the first order of business to measure the soft breaking parameters. But one will also want to understand the symmetry, and its breaking, more microscopically. Two aspects of this problem constitute the focus of these lectures. First, what sorts of dynamics might account for supersymmetry breaking, and its manifestation at low energies. Second, how might these features fit into string theory (or whatever might be the underlying theory in the ultraviolet). The last few years have seen a much improved understanding of the first set of questions, and at least a possible pathway to address the second.

The article is quite pedagogical, and even begins with an ultra fast introduction to supersymmetry. Certainly recommendable.

On the subject of supersymmetry in the LHC era I thing that everybody would must read the last entry of Jester's blog: What LHC tells about SUSY that discussed the paper of the ATLAS collaboration: Search for supersymmetry using final states with one lepton, jets, and missing transverse momentum with the ATLAS detector in sqrt{s} = 7 TeV pp.

Well, certainly the expectations of Lubos of an early discovery of SUSY in the LHC are gone, but still there are good reasons to be patient, as explained by Lubos himself or by the Dine's paper.

By the way, while writing this entry I have seen that Lubos himself has written an entry about the Dines paper, you can read it here. At the moment of writing my entry he hasn't given many details about the article, but possibly he will edit his post and discuss the paper in more detail.

Update: Lubos has read this entry and has written a very intersting essay about the general relevance (or irrelevance) of the pathological mathematical structures in physics .

About the actual series of papers in exotic R^4 he doesn't say too much because he claims that he doesn't understand the paper. I have been studying the subject, including some references, and I am still going on. Much of the mathematics (differential topology: h-cobordism, topological surgery, tubular neighbourhoods) are familiar to me, but some more recent concepts are new to me. Still I think that I can follow the general argumentative line of the mat part. I get somewhat more loose in other points of the WZW model in an SU(2) background, but still I think that I get the general argumentation. As soon as I end reading a few more references I'll try to expose the key ideas.

Anyway, there is a difference here with the case commented but Lubos. R^4 is the only R^n that admits different smooth structures for the same topological structure. In that aspect it is not a case of searching for a pathology but a case where the pathology appears by itself. In fact most people who have heard about that particularity of R^4 have always though that maybe that could be the ultimate reason that we live in a four dimensional manifold. Of course what they lacked is a way to relate that peculiarity of R^4 to any actual physic. This people seem to have advanced somewhat in that direction, but as far as I understood they are far of the objective (if that is their objective, that probably it is not the case).

The article is actually the second part of a previous one: Exotic smooth R^4 and certain configurations of NS and D branes in string theory.

The abstract of the first (in date order) article reads:

In this paper we show that in some important cases 4-dimensional data can be extracted from superstring theory such that a) the data are 4 Euclidean geometries embedded in standard $\mathbb{R}^{4}$, b) these data depend on NS and D brane charges of some string backgrounds, c) it is of potential relevance to 4-dimensional physics, d) the compactification and stabilization techniques are not in use, but rather are replaced. We analyze certain configurations of NS and D-branes in the context of $SU(2)$ WZW model and find the correlations with different exotic smoothings of $\mathbb{R}^{4}$. First, the dynamics of D-branes in $SU(2)$ WZW model at finite $k$, i.e. the charges of the branes, refers to the exoticness of ambient $\mathbb{R}^{4}$. Next, the correspondence between exotic smoothness on 4-space, transversal to the world volume of NS5 branes in IIA type, and the number of these NS5 branes follows. Finally, the translation of 10 dimensional string backgrounds to 4 Euclidean spaces embedded as open subsets in the standard $\mathbb{R}^{4}$ is achieved.

I still haven't had time to read the full article, but it looks quite interesting, and beautifully, specially from the perspective of someone whose favourite area of maths is topology. The idea is to see if someone can make string theory in a background of R^4 with a different differential structure than the usual one. One of the most amazing discoveries of differential topology was that there were different differential structures for R^4 than the usual one. That means that although like a topological manifold R^4 is unique there are different differentiable manifolds that are compatible with it's topological structure. An explicit characterization of that exotic structures in terms of coordinate is difficult and their existence is proved by means of topological techniques. In the paper it is made use of h-cobordism.

Later he begins the string theoretical construction, using SU(2) WZW (wess-zumino-witten= CFT's, NS 5 branes, D branes, etc. AS I still haven't read the article carefully, nor the continuation of it (the today's arxiv article ) wouldn't give more details. Only to say that it looks like a very intriguing area of research.

Also today in arxiv there is a very interesting, but much more conventional article of Miche Dine: Supersymmetry from the Top Down whose abstract is:

If supersymmetry turns out to be a symmetry of nature at low energies, the first order of business to measure the soft breaking parameters. But one will also want to understand the symmetry, and its breaking, more microscopically. Two aspects of this problem constitute the focus of these lectures. First, what sorts of dynamics might account for supersymmetry breaking, and its manifestation at low energies. Second, how might these features fit into string theory (or whatever might be the underlying theory in the ultraviolet). The last few years have seen a much improved understanding of the first set of questions, and at least a possible pathway to address the second.">If supersymmetry turns out to be a symmetry of nature at low energies, the first order of business to measure the soft breaking parameters. But one will also want to understand the symmetry, and its breaking, more microscopically. Two aspects of this problem constitute the focus of these lectures. First, what sorts of dynamics might account for supersymmetry breaking, and its manifestation at low energies. Second, how might these features fit into string theory (or whatever might be the underlying theory in the ultraviolet). The last few years have seen a much improved understanding of the first set of questions, and at least a possible pathway to address the second.

The article is quite pedagogical, and even begins with an ultra fast introduction to supersymmetry. Certainly recommendable.

On the subject of supersymmetry in the LHC era I thing that everybody would must read the last entry of Jester's blog: What LHC tells about SUSY that discussed the paper of the ATLAS collaboration: Search for supersymmetry using final states with one lepton, jets, and missing transverse momentum with the ATLAS detector in sqrt{s} = 7 TeV pp.

Well, certainly the expectations of Lubos of an early discovery of SUSY in the LHC are gone, but still there are good reasons to be patient, as explained by Lubos himself or by the Dine's paper.

By the way, while writing this entry I have seen that Lubos himself has written an entry about the Dines paper, you can read it here. At the moment of writing my entry he hasn't given many details about the article, but possibly he will edit his post and discuss the paper in more detail.

Update: Lubos has read this entry and has written a very intersting essay about the general relevance (or irrelevance) of the pathological mathematical structures in physics .

About the actual series of papers in exotic R^4 he doesn't say too much because he claims that he doesn't understand the paper. I have been studying the subject, including some references, and I am still going on. Much of the mathematics (differential topology: h-cobordism, topological surgery, tubular neighbourhoods) are familiar to me, but some more recent concepts are new to me. Still I think that I can follow the general argumentative line of the mat part. I get somewhat more loose in other points of the WZW model in an SU(2) background, but still I think that I get the general argumentation. As soon as I end reading a few more references I'll try to expose the key ideas.

Anyway, there is a difference here with the case commented but Lubos. R^4 is the only R^n that admits different smooth structures for the same topological structure. In that aspect it is not a case of searching for a pathology but a case where the pathology appears by itself. In fact most people who have heard about that particularity of R^4 have always though that maybe that could be the ultimate reason that we live in a four dimensional manifold. Of course what they lacked is a way to relate that peculiarity of R^4 to any actual physic. This people seem to have advanced somewhat in that direction, but as far as I understood they are far of the objective (if that is their objective, that probably it is not the case).

Etiquetas:
string theory,
topolgy

## Friday, February 11, 2011

### String theory and nanotechnology meet today in arxiv

String theory deal mainly with physic at the planck scale, although it's goal is to connect to with the electroweak scale.

On the other hand, nonotehcnology, deals with physics at sizes similar to the Bohr radius. There are, consequently, many orders of magnitude of difference among that two branches of physics.

Because of that it is absolutely amazing to see in the title of the paper a reference to a relation among them. But today in arxiv we have such a paper: Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes.

The abstract reads like this:

We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive fermionic field in the geometry of two parallel plate on the background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions, in the presence of a constant gauge field. Bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The boundary induced parts in the fermionic condensate and the vacuum energy density are negative, with independence of the phases in the periodicity conditions and of the value of the gauge potential. Interaction forces between the plates are thus always attractive. However, in physical situations where the quantum field is confined to the region between the plates, the pure topological part contributes as well, and then the resulting force can be either attractive or repulsive, depending on the specific phases encoded in the periodicity conditions along the compact dimensions, and on the gauge potential, too. Applications of the general formulas to cylindrical carbon nanotubes are considered, within the framework of a Dirac-like theory for the electronic states in graphene. In the absence of a magnetic flux, the energy density for semiconducting nanotubes is always negative. For metallic nanotubes the energy density is positive for long tubes and negative for short ones. The resulting Casimir forces acting on the edges of the nanotube are attractive for short tubes with independence of the tube chirality. The sign of the force for long nanotubes can be controlled by tuning the magnetic flux. This opens the way to the design of efficient actuators driven by the Casimir force at the nanoscale.

I haven't read in deep the paper, but in a superficial reading I have got a confirmation that they are actually claiming that actual aspects of the compactified extra dimensions of string theory could, through the Casimir effect observable consequences in the characteristics of nanotechnologic materials, in particular nanotubes. My guess is that there must be some error, or some trick, somewhere. If not this paper would be driving string theory from the realms of cute edge speculative high energy physics to actual applications in one of the most economicaly profitable industries. Too good to be truth probably, but, who knows? Well, I'll read the article carefully sooner and I'll comment more details. But I doubt that I would be the only one to say something about it ;)-

Update: Ok, the article actually doesn't relate string theory extra dimensions and carbone nanotubes. IT only applies the formalism of compactificactions to nanotubes, based on the premise that a nanotube is a cylinder, i.e. a compactified plane. The introductions, and many other parts of the article are somewhat misleading and seem to suggest what I had explained. Also it is misleading the fact that it appears inhep-th. The reason for that possibly is that they make some development of the formalism of compactifications in a general, multidimensional, framework. Possibly that general development could be usefull for people working in string theory, that possibly justifies the inclussion of the paper in hep-th although the primal subjecto of the paper is condensed matter physic.

On the other hand, nonotehcnology, deals with physics at sizes similar to the Bohr radius. There are, consequently, many orders of magnitude of difference among that two branches of physics.

Because of that it is absolutely amazing to see in the title of the paper a reference to a relation among them. But today in arxiv we have such a paper: Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes.

The abstract reads like this:

We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive fermionic field in the geometry of two parallel plate on the background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions, in the presence of a constant gauge field. Bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The boundary induced parts in the fermionic condensate and the vacuum energy density are negative, with independence of the phases in the periodicity conditions and of the value of the gauge potential. Interaction forces between the plates are thus always attractive. However, in physical situations where the quantum field is confined to the region between the plates, the pure topological part contributes as well, and then the resulting force can be either attractive or repulsive, depending on the specific phases encoded in the periodicity conditions along the compact dimensions, and on the gauge potential, too. Applications of the general formulas to cylindrical carbon nanotubes are considered, within the framework of a Dirac-like theory for the electronic states in graphene. In the absence of a magnetic flux, the energy density for semiconducting nanotubes is always negative. For metallic nanotubes the energy density is positive for long tubes and negative for short ones. The resulting Casimir forces acting on the edges of the nanotube are attractive for short tubes with independence of the tube chirality. The sign of the force for long nanotubes can be controlled by tuning the magnetic flux. This opens the way to the design of efficient actuators driven by the Casimir force at the nanoscale.

I haven't read in deep the paper, but in a superficial reading I have got a confirmation that they are actually claiming that actual aspects of the compactified extra dimensions of string theory could, through the Casimir effect observable consequences in the characteristics of nanotechnologic materials, in particular nanotubes. My guess is that there must be some error, or some trick, somewhere. If not this paper would be driving string theory from the realms of cute edge speculative high energy physics to actual applications in one of the most economicaly profitable industries. Too good to be truth probably, but, who knows? Well, I'll read the article carefully sooner and I'll comment more details. But I doubt that I would be the only one to say something about it ;)-

Update: Ok, the article actually doesn't relate string theory extra dimensions and carbone nanotubes. IT only applies the formalism of compactificactions to nanotubes, based on the premise that a nanotube is a cylinder, i.e. a compactified plane. The introductions, and many other parts of the article are somewhat misleading and seem to suggest what I had explained. Also it is misleading the fact that it appears inhep-th. The reason for that possibly is that they make some development of the formalism of compactifications in a general, multidimensional, framework. Possibly that general development could be usefull for people working in string theory, that possibly justifies the inclussion of the paper in hep-th although the primal subjecto of the paper is condensed matter physic.

## Thursday, January 27, 2011

### Two cosmology papes and the question of extra dimensions

First an advert, the two topics are unrelated, well, or may be not ;).

The first paper I would want to mention is this form Luis Alvarez Gaumé. Gaumé is one of the best known spanish string theorists. He is famous for the 80's paper with Witten about the (absence of) anomalies in string theory.

Now he has a paper in arxiv. A Minimal Inflation Scenario. This is the abstract:

We elaborate on a minimal inflation scenario based entirely on the general properties of supersymmetry breaking in supergravity models. We identify the inflaton as the scalar component of the Goldstino superfield. We write plausible candidates for the effective action describing this chiral superfield. In particular the theory depends (apart from parameters of O(1)) on a single free parameter: the scale of supersymmetry breaking. This can be fixed using the amplitude of CMB cosmological perturbations and we therefore obtain the scale of supersymmetry breaking to be 10^{12-14} GeV. The model also incorporates explicit R-symmetry breaking in order to satisfy the slow roll conditions. In our model the eta-problem is solved without extra fine-tuning. We try to obtain as much information as possible in a model independent way using general symmetry properties of the theory's effective action, this leads to a new proposal on how to exit the inflationary phase and reheat the Universe.

I am far from expert in the inflation technicalities but it looks like a quite natural proposal (well, maybe except for explicit R-parity breaking, which, otherwise, is good for some very specific models of dark matter tht were popular the last year trying to accommodate some now not too much discussed anomalies from PAMELA, ARTIC and others).

The other cosmology paper I wanted to mention is this: Holographic unification of dark matter and dark energy. The abstract is as follows: Using a new version of the holographic principle, a constant term was introduced, which conduces to the description of the standard cosmological LCDM model, and unifies under the same concept the dark matter and dark energy phenomena. The obtained model improves the results of previously considered holographic models based on local quantities. The inclusion of constant term is interpreted as a natural first approximation for the infrared cutoff which is associated with the vacuum energy, and the additional terms guarantee an appropriate evolutionary scenario that fits the astrophysical observations. The model allows to reproduce the standard LCDM model without explicitly introducing matter content, and using only geometrical quantities. It is also obtained that the model may describe the dark energy beyond the standard LCDM.

The idea of unifying dark matter and dark energy as one and the same phenomena looks interesting aesthetically. Against it it is the question of many independent observations leading to the existence of dark matter. Specially he galactic ones seem a little bit out of the sight of this paper. But I remember a paper a few time ago that could fit the rotation of galaxies by mean of an stringy phenomena without need of dark matter. Still there is a good reason for expecting the existence of dark matter: Supersymmetry. Specially if R-parity is conserved the LSP is stable and would be a component of dark matter. And one expect that supersymmetry would break near the electroweak scale, isn't it?

Well, maybe. But one of the main supports of low energy SSB is the resolution of the hierarchy problem. Fortunately there is another option for solving the hierarchy problem, the Randall-Sumdrum scenaries. Recently there were two results from the tevatron announcing two anomalies at more than 3 sigmas related to top quark physics. One is described in the article: Evidence for a Mass Dependent Forward-Backward Asymmetry in Top Quark Pair Production., Annalized in entries in the Lubos and Jester blog, among others.

The other, more recent one, was first announced in the Jester's blog: Another Intriguing Result from Tevatron's CDF that also was analysed in Lubos blog (I don' put the link because everybody reads Lubos blog, isn't it? ;) ).

Reading the entries, and the comments one sees that there is a main natural candidate for both phenomena, a KK (kaluza-klein) partner of the gluon. For that KK gluon being in the right track one must be in a Randall-Sumdrum scenario. That means that if the LHC, that restart it's operation in fabruary, confirms the anomalies we would have a (very likely) confirmation of the existence of extra dimensions which would be possibly the most amazing all times experimental discovery in physics.

But don't shout Eureka still. Recently the LHC published an article advertising that they had not seen evidence of micro black holes, which is a bad thing for the R-S sceneries. Well, one wouldn't care too much about it. Microscopic B-h are not the former prediction of R-S scenaries and the paper had some drawbacks also.

Yesterday there was a paper about this R-S braneworlds proposal and it's measure in the LHC: LHC bounds on large extra dimensions based on the analysis of 3.1 inverse picobarns of LHC data that fixed new limits in the possible extent of the extra dimensions. AS far as I understand that bounds don't forbid the KK gluon as the author of the top quarks anomalies. Of course there are another possible answers to that anomalies. For example Marco Frasca claims (The Tevatron affair and the “fat” gluon )that his model of "fat gluon" could do the job (although he acknowledges that the KK gluon fits better).

Well, the thing is that if braneworlds are proved valid the motivation for weak scale SSB would be lacking (because R-S would solve the hierarchy problem), and with it the best candidates for dark matter. Still one could think that another KK particle are candidates for dark matter. But maybe the theories that unifies dark matter and dark energy would gain some points, or maybe be not, cosmology you know ;).

The first paper I would want to mention is this form Luis Alvarez Gaumé. Gaumé is one of the best known spanish string theorists. He is famous for the 80's paper with Witten about the (absence of) anomalies in string theory.

Now he has a paper in arxiv. A Minimal Inflation Scenario. This is the abstract:

We elaborate on a minimal inflation scenario based entirely on the general properties of supersymmetry breaking in supergravity models. We identify the inflaton as the scalar component of the Goldstino superfield. We write plausible candidates for the effective action describing this chiral superfield. In particular the theory depends (apart from parameters of O(1)) on a single free parameter: the scale of supersymmetry breaking. This can be fixed using the amplitude of CMB cosmological perturbations and we therefore obtain the scale of supersymmetry breaking to be 10^{12-14} GeV. The model also incorporates explicit R-symmetry breaking in order to satisfy the slow roll conditions. In our model the eta-problem is solved without extra fine-tuning. We try to obtain as much information as possible in a model independent way using general symmetry properties of the theory's effective action, this leads to a new proposal on how to exit the inflationary phase and reheat the Universe.

I am far from expert in the inflation technicalities but it looks like a quite natural proposal (well, maybe except for explicit R-parity breaking, which, otherwise, is good for some very specific models of dark matter tht were popular the last year trying to accommodate some now not too much discussed anomalies from PAMELA, ARTIC and others).

The other cosmology paper I wanted to mention is this: Holographic unification of dark matter and dark energy. The abstract is as follows: Using a new version of the holographic principle, a constant term was introduced, which conduces to the description of the standard cosmological LCDM model, and unifies under the same concept the dark matter and dark energy phenomena. The obtained model improves the results of previously considered holographic models based on local quantities. The inclusion of constant term is interpreted as a natural first approximation for the infrared cutoff which is associated with the vacuum energy, and the additional terms guarantee an appropriate evolutionary scenario that fits the astrophysical observations. The model allows to reproduce the standard LCDM model without explicitly introducing matter content, and using only geometrical quantities. It is also obtained that the model may describe the dark energy beyond the standard LCDM.

The idea of unifying dark matter and dark energy as one and the same phenomena looks interesting aesthetically. Against it it is the question of many independent observations leading to the existence of dark matter. Specially he galactic ones seem a little bit out of the sight of this paper. But I remember a paper a few time ago that could fit the rotation of galaxies by mean of an stringy phenomena without need of dark matter. Still there is a good reason for expecting the existence of dark matter: Supersymmetry. Specially if R-parity is conserved the LSP is stable and would be a component of dark matter. And one expect that supersymmetry would break near the electroweak scale, isn't it?

Well, maybe. But one of the main supports of low energy SSB is the resolution of the hierarchy problem. Fortunately there is another option for solving the hierarchy problem, the Randall-Sumdrum scenaries. Recently there were two results from the tevatron announcing two anomalies at more than 3 sigmas related to top quark physics. One is described in the article: Evidence for a Mass Dependent Forward-Backward Asymmetry in Top Quark Pair Production., Annalized in entries in the Lubos and Jester blog, among others.

The other, more recent one, was first announced in the Jester's blog: Another Intriguing Result from Tevatron's CDF that also was analysed in Lubos blog (I don' put the link because everybody reads Lubos blog, isn't it? ;) ).

Reading the entries, and the comments one sees that there is a main natural candidate for both phenomena, a KK (kaluza-klein) partner of the gluon. For that KK gluon being in the right track one must be in a Randall-Sumdrum scenario. That means that if the LHC, that restart it's operation in fabruary, confirms the anomalies we would have a (very likely) confirmation of the existence of extra dimensions which would be possibly the most amazing all times experimental discovery in physics.

But don't shout Eureka still. Recently the LHC published an article advertising that they had not seen evidence of micro black holes, which is a bad thing for the R-S sceneries. Well, one wouldn't care too much about it. Microscopic B-h are not the former prediction of R-S scenaries and the paper had some drawbacks also.

Yesterday there was a paper about this R-S braneworlds proposal and it's measure in the LHC: LHC bounds on large extra dimensions based on the analysis of 3.1 inverse picobarns of LHC data that fixed new limits in the possible extent of the extra dimensions. AS far as I understand that bounds don't forbid the KK gluon as the author of the top quarks anomalies. Of course there are another possible answers to that anomalies. For example Marco Frasca claims (The Tevatron affair and the “fat” gluon )that his model of "fat gluon" could do the job (although he acknowledges that the KK gluon fits better).

Well, the thing is that if braneworlds are proved valid the motivation for weak scale SSB would be lacking (because R-S would solve the hierarchy problem), and with it the best candidates for dark matter. Still one could think that another KK particle are candidates for dark matter. But maybe the theories that unifies dark matter and dark energy would gain some points, or maybe be not, cosmology you know ;).

Etiquetas:
cosmology,
Kaluza-Klein

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