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 ${\mathrm{AdS}}_5\times S^5$. 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.

• Received 6 May 2006

DOI:https://doi.org/10.1103/PhysRevD.74.026002