http://arxiv.org/abs/1207.4657
Signature change in loop quantum cosmology
Jakub Mielczarek
(Submitted on 19 Jul 2012)
The Wick rotation is commonly considered only as an useful computational trick. However, as it was suggested by Hartle and Hawking already in early eighties, Wick rotation may gain physical meaning at the Planck epoch. While such possibility is conceptually interesting, leading to no-boundary proposal, mechanism behind the signature change remains mysterious. We show that the signature change anticipated by Hartle and Hawking naturally appear in loop quantum cosmology. Theory of cosmological perturbations with the effects of quantum holonomies is discussed. It was shown by Cailleteau \textit{et al.} (Class. Quant. Grav. {\bf 29} (2012) 095010) that this theory can be uniquely formulated in the anomaly-free manner. The obtained algebra of effective constraints turns out to be modified such that the metric signature is changing from Lorentzian in low curvature regime to Euclidean in high curvature regime. Implications of this phenomenon on propagation of cosmological perturbations are discussed and corrections to inflationary power spectra of scalar and tensor perturbations are derived. Possible relations with other approaches to quantum gravity are outlined. We also propose an intuitive explanation of the observed signature change using analogy with spontaneous symmetry breaking in "wired" metamaterials.
http://arxiv.org/abs/1207.4503
Spontaneous Dimensional Reduction?
S. Carlip
(Submitted on 18 Jul 2012)
Over the past few years, evidence has begun to accumulate suggesting that spacetime may undergo a "spontaneous dimensional reduction" to two dimensions near the Planck scale. I review some of this evidence, and discuss the (still very speculative) proposal that the underlying mechanism may be related to short-distance focusing of light rays by quantum fluctuations
http://arxiv.org/abs/1207.4603
Towards superconformal and quasi-modular representation of exotic smooth R^4 from superstring theory II
Torsten Asselmeyer-Maluga, Jerzy Król
(Submitted on 19 Jul 2012)
This is the second part of the work where quasi-modular forms emerge from small exotic smooth $\mathbb{R}^4$'s grouped in a fixed radial family. SU(2) Seiberg-Witten theory when formulated on exotic $\mathbb{R}^4$ from the radial family, in special foliated topological limit can be described as SU(2) Seiberg-Witten theory on flat standard $\mathbb{R}^4$ with the gravitational corrections derived from coupling to ${\cal N}=2$ supergravity.
Formally, quasi-modular expressions which follow the Connes-Moscovici construction of the universal Godbillon-Vey class of the codimension-1 foliation, are related to topological correlation functions of superstring theory compactified on special Callabi-Yau manifolds. These string correlation functions, in turn, generate Seiberg-Witten prepotential and the couplings of Seiberg-Witten theory to ${\cal N}=2$ supergravity sector. Exotic 4-spaces are conjectured to serve as a link between supersymmetric and non-supersymmetric Yang-Mills theories in dimension 4.
http://arxiv.org/abs/1207.4602
Towards superconformal and quasi-modular representation of exotic smooth R^4 from superstring theory I
Torsten Asselmeyer-Maluga, Jerzy Król
(Submitted on 19 Jul 2012)
We show that superconformal ${\cal N}=4,2$ algebras are well-suited to represent some invariant constructions characterizing exotic $\mathbb{R}^4$ relative to a given radial family. We examine the case of ${\cal N}=4, \hat{c}=4$ (at $r=1$ level) superconformal algebra which is realized on flat $\mathbb{R}^4$ and curved $S^3\times \mathbb{R}$. While the first realization corresponds naturally to standard smooth $\mathbb{R}^4$ the second describes the algebraic end of some small exotic smooth $\mathbb{R}^4$'s from the radial family of DeMichelis-Freedman and represents the linear dilaton background $SU(2)_k\times \mathbb{R}_Q$ of superstring theory.
From the modular properties of the characters of the algebras one derives Witten-Reshetikhin-Turaev and Chern-Simons invariants of homology 3-spheres. These invariants are represented rather by false, quasi-modular, Ramanujan mock-type functions. Given the homology 3-spheres one determines exotic smooth structures of Freedman on $S^3\times \mathbb{R}$. In this way the fake ends are related to the SCA ${\cal N}=4$ characters.
The case of the ends of small exotic $\mathbb{R}^4$'s is more complicated. One estimates the complexity of exotic $\mathbb{R}^4$ by the minimal complexity of some separating from the infinity 3-dimensional submanifold. These separating manifolds can be chosen, in some exotic $\mathbb{R}^4$'s, to be homology 3-spheres. The invariants of such homology 3-spheres are, again, obtained from the characters of SCA, ${\cal N}=4$.
