Supersymmteric Null-like Holographic Cosmologies

TL;DR

The paper addresses quantum cosmology near the big bang by constructing a class of $1/4$-BPS, null-like domain-wall solutions in type II supergravity that yield a null-like big bang singularity. It develops the domain-wall/QFT framework to describe a $d=2$ dual field theory on a time-dependent boundary cosmology with evolving coupling and UV cutoff, and computes a holographic $c$-function that runs with the boundary evolution and diverges at the big bang, suggesting a potential singularity-resolution mechanism. The main contributions include explicit null-like domain-wall solutions, a Friedman-like boundary cosmology, a detailed Killing-spinor analysis showing $1/4$ supersymmetry, and a concrete holographic $c$-function with frame-dependent but consistent behavior under frame transformations. The work offers a robust holographic setup to study time-dependent strongly coupled QFTs in cosmological backgrounds and motivates future investigations into correlators, S-duality, and extensions to other $p$-brane setups.

Abstract

We construct a new class of 1/4-BPS time dependent domain-wall solutions with null-like metric and dilaton in type II supergravities, which admit a null-like big bang singularity. Based on the domain-wall/QFT correspondence, these solutions are dual to 1/4-supersymmetric quantum field theories living on a boundary cosmological background with time dependent coupling constant and UV cutoff. In particular we evaluate the holographic $c$ function for the 2-dimensional dual field theory living on the corresponding null-like cosmology. We find that this $c$ function runs in accordance with the $c$-theorem as the boundary universe evolves, this means that the number of degrees of freedom is divergent at big bang and suggests the possible resolution of big bang singularity.