Gauge Theory Duals of Cosmological Backgrounds and their Energy Momentum Tensors

TL;DR

The paper investigates Type IIB supergravity backgrounds with null and spacelike cosmological singularities and constructs dual gauge theories living on flat spacetime with spacetime-dependent couplings $g_{YM}(x)=e^{\frac{\Phi(x)}{2}}$. It develops a PBH-based coordinate framework to realize flat-boundary holographic duals for null and Kasner-type solutions, and introduces a new FRW-inspired time-dependent class with bounded coupling that vanishes at a bulk singularity. The holographic stress tensor is computed using covariant counterterms, revealing vanishing $\langle T^{\mu\nu}\rangle$ for null backgrounds and nonzero, often divergent, expectations for time-dependent cases, with traces matching known holographic anomalies. Overall, the work clarifies how gauge theories with time- or null-dependent couplings can provide a controlled holographic description near cosmological singularities, while also highlighting limitations imposed by bulk singularities on the gravity side.

Abstract

We revisit Type IIB supergravity backgrounds with null and spacelike singularities with natural gauge theory duals proposed in {\tt hep-th/0602107} and {\tt hep-th/0610053}. We show that for these backgrounds there are always choices of the boundaries of these deformed $AdS_5 \times S^5$ space-times, such that the dual gauge theories live on {\it flat} metrics and have space-time dependent couplings. We present a new time dependent solution of this kind where the effective string coupling is always bounded and vanishes at a spacelike singularity in the bulk, and the space-time becomes $AdS_5 \times S^5$ at early and late times. The holographic energy momentum tensor calculated with a choice of flat boundary is shown to vanish for null backgrounds and to be generically non-zero for time dependent backgrounds.