Time-dependent cosmologies and their duals

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 ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$. Several of the solutions have singularities. The light-like solutions preserve 8 supersymmetries. We argue that these solutions are dual to the $\mathcal{N}=4$ gauge theory in a $3+1$ dimensional space-time 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.