## Wednesday, June 07, 2006

### Hep-th papers on Wednesday

Ioannis Papadimitriou constructs new domain-wall-like solutions that are asymptotic to the near-horizon geometry of M2-branes, namely "AdS4 x S7" (supergravity in four noncompact dimensions). He uses the method of "fake supergravity".

Han-Xin He claims that he or she has calculated the full, exact three-point function of two fermionic fields and one gauge field in QED, just by algebraic manipulations with the Ward-Takahishi identities. An anonymous reader has pointed out that the resulting formula depends on the full non-perturbative fermionic propagator, so it is not quite a "free lunch", but it still seems nontrivial. The result has been checked up to one-loop level but it seems that it is being argued that it is valid up to all orders. This sounded like an extraordinary statement, especially because the formulae didn't seem to have the complexity and transcendentality of the higher-loop contributions, but I am not able to say what's wrong with it. If it's correct, it means that all the complexities of the fermion propagator and the three-point function are isomorphic. Comments will be certainly welcome.

Shinji Tsukikawa studies how the higher-derivative corrections to general relativity arising from string theory may regulate the Big Bang singularity and generate various bouncing, ekpyrotic, and other solutions. Topics of this kind were very popular five years ago. Do you remember papers such as Seiberg's paper on the Big Bounce?

Shibaji Roy and Harvendra Singh propose a technique to generate accelerating cosmological solutions from "S-branes" of another kind that has not yet been used. I have not understood how can one decide whether something is an S-brane or not. S-branes seem to be a label for rather general time-dependent solutions, unlike D-branes that are the lowest energy states in a given charge sector. This makes it difficult for me to understand why a solution should become important just because it is connected with the term "S-brane". The only meaningful purely spacelike counterpart of D-branes is a D-instanton or D-brane-instanton which is just a continuation of the usual D-branes to a Euclidean spacetime. S-branes are supposed to be something else but I don't think there is any room for something else.

Giuseppe Bimonte, Enrico Calloni, Giampiero Esposito, and Luigi Rosa include the first-order corrections from a gravitational field to a conventional calculation of the Casimir effect. They must be computing the first subleading correction, I think. Up to the leading order, the Casimir force and the gravitational force are simply added together. They argue that the Casimir force becomes a little bit stronger if you add acceleration (or gravity).

T.Khachidze, A. Khelashvili, T.Nadareishvili only offer a PDF file, and they argue that the Dirac equation does not reduce to the usual non-relativistic equation in the appropriate limit. They say that it has extra solutions - maybe hydrinos? :-) - and some new qualitative features. I am convinced that their paper is based on elementary errors. For example, when they square the Dirac Hamiltonian, they only keep the "V^2" terms but omit the main term proportional to "V" that actually survives in the Schrödinger limit. The "V^2" term is only a relativistic correction, analogous to the "p^4" corrections to the kinetic energy. The authors are recommended to study the derivation of the non-relativistic limit of the Dirac equation from one of the standard textbooks.

Daniel Litim promotes the idea that the UV fixed point of general relativity exists. An ultraviolet fixed point is the hypothetical scale-invariant theory valid at the sub-Planckian distances whose relevant deformation turns flows to general relativity at long distances. Its existence could make quantized general relativity predictive but it is believed that such a fixed point does not exist. Litim admits that classically, such a scale-invariant theory only exists in the critical dimension "d=2". We know purely field-theoretical gravitational theories in this spacetime dimension; the most useful two-dimensional field-theoretical gravity in "d=2" is called the string worldsheet. However, Litim claims that a fixed point of the renormalization group exists in every dimension. To support this claim, he considers the cosmological constant (Lambda) and the Einstein-Hilbert term (G) only, and studies the evolution of "Lambda,G" under the RG flow. With an appropriately chosen anomalous dimensions of the operators, he can find a fixed point in every dimension. I find this argument unconvincing because in the sub-Planckian distance regime, gravity is strongly coupled and it is not justified to neglect all other terms except for "Lambda,G". Equivalently, we can see that the "Lambda,G" approximation is bad because the anomalous dimensions of the fields are greater than one. It is unsurprising that whenever we include a few couplings only, we will formally find some fixed points, but those that appear in strongly coupled regions of the parameter space can't be quite trusted, unless a more complete argument is found.

Itzhak Bars continues in his provoking research of physics with two time coordinates. Today, he considers the Standard Model derived from a 4+2-dimensional starting point. In the past, Bars has argued that one can obtain very different physical systems - such as the Hydrogen atom and the harmonic oscillator - by different gauge-fixing choices applied to the same double-temporal starting point with an Sp(2,R) gauge symmetry. I don't understand how can one ever get different physics by choosing a gauge-fixing condition. Gauge symmetry and gauge-fixing choices should not affect observable physics, by definition. This is why I can't quite understand either of Bars' two-time papers. Nevertheless, if someone can do better than me, this paper constructs the Standard Model from a 4+2-dimensional starting point. Not only that, it explains the strong CP-problem because the "F /\ F" term cannot arise in this framework.

Martin Land discusses aspects of generalized D-dimensional Dirac magnetic monopole. I feel 85% certain that if you know Maxwell's equations in D dimensions and the simple power law solutions for electric and magnetic point-like sources, you won't find anything new in this paper.

Gottfried Curio and Vera Spillner jump into a seemingly random place of the KKLT landscape. They start with the elliptic Calabi-Yau manifold called P_{11169}[18] - known from "building a better racetrack" - and write down all relevant terms in the superpotential that is usually used in the context of flux compactifications, coming from fluxes and gaugino condensation. They modify the usual wisdoms by an unexpected dependence on the dilaton "tau". They seem to argue that the superpotential "W(tau)" itself is not holomorphic which I misunderstand because superpotentials should be holomophic. But because they seem to be really powerful technologically, I am inclined to believe that the paper makes a perfect sense.

Kazumi Okuyama studies the topological partition sum on the conifold - both in the A-model (the math of melting crystals) as well as B-model (Chern-Simons matrix model). He or she finds a very interesting integral transform that transform one to the other. The integral transform involves an integral over matrices with a Gaussian measure.

U. Gran, J. Gutowski, G. Papadopoulos, D. Roest argue that there are no configurations with exactly 31 supercharges in type IIB supergravity. More precisely, if you give them one with 31 supercharges, they are able to find the 32nd supercharge, proving that the background is maximally supersymmetric. It is analogous to "N=7" theories in "d=4" that are automatically "N=8", too. Their finding, if correct, invalidates the type IIB version of the "preon" speculation. These "preons", in the SUGRA context, were proposed to preserve 31 supercharges. Their central charge was hypothesized to be a "32 x 32" matrix whose rank equals one (instead of more usual values such as 16) which could turn them into basic building blocks of other systems that preserve a smaller number of supercharges. Such a bizarre rank-one central charge would clearly be a combination of central charges associated with branes of all possible dimensions, and this paper shows that this can't work at the level of type IIB supergravity.