Time Dependent Cosmologies and Their Duals

TL;DR

This work addresses how to understand time-dependent and null cosmological singularities within string theory and their holographic duals by constructing a broad class of Type IIB supergravity solutions that deform $AdS_5\times S^5$. The authors develop solutions with a warp factor $Z$, harmonic transverse space, and a dilaton, showing that Kasner-like time dependence and light-like dependence can be accommodated, with near-horizon limits yielding holographic backgrounds governed by a 4D Einstein-dilaton system. They establish that null backgrounds preserve 8 supersymmetries and map bulk deformations to time-dependent or light-like sources in ${\mathcal{N}}=4$ SYM, including operator correspondences such as ${\rm Tr} F^2$ and the stress tensor $T_{\mu\nu}$, and discuss conformal anomalies as indicators of gauge theory behavior near singularities. The analysis highlights how singular bulk dynamics may be reflected in the dual gauge theory and points to scenarios where the gauge theory remains well-behaved, especially in certain null, conformally flat cases, while suggesting extensions to other AdS geometries like $AdS_3\times S^3$ for further study. Overall, the paper provides a holographic framework to probe cosmological singularities and their potential resolution through the dual gauge theory.

Abstract

We construct a family of solutions in IIB supergravity theory. These are time dependent or depend on a light-like coordinate and can be thought of as deformations of AdS_5 x S^5. Several of the solutions have singularities. The light-like solutions preserve 8 supersymmetries. We argue that these solutions are dual to the N=4 gauge theory in a 3+1 dimensional spacetime with a metric and a gauge coupling that is varying with time or the light-like direction respectively. This identification allows us to map the question of singularity resolution to the dual gauge theory.