Time-dependent AdS/CFT Duality II: Holographic Reconstruction of Bulk Metric and Possible Resolution of Singularity

TL;DR

This paper advances the holographic duality for time-dependent backgrounds, demonstrating how boundary gauge theory effective actions can reconstruct bulk metrics and potentially resolve singularities through quantum effects.

Contribution

It introduces a method to reconstruct the bulk metric from boundary effective actions in time-dependent AdS/CFT setups and suggests quantum corrections can resolve singularities.

Findings

Bulk metric can be reconstructed from Wilsonian effective action.

Quantum effects in gauge theory can resolve bulk singularities.

The approach enables detailed perturbative analysis of time-dependent backgrounds.

Abstract

We continue the studies of our earlier proposal for an AdS/CFT correspondence for time-dependent supergravity backgrounds. We note that by performing a suitable change of variables, the dual super Yang-Mills theory lives on a flat base space, and the time-dependence of the supergravity background is entirely encoded in the time-dependent couplings (gauge and axionic) and their supersymmetric completion. This form of the SYM allows a detailed perturbative analysis to be performed. In particular the one-loop Wilsonian effective action of the boundary SYM theory is computed. By using the holographic UV/IR relation, we propose a way to extract the bulk metric from the Wilsonian effective action; and we find that the bulk metric of our supergravity solutions can be reproduced precisely. While the bulk geometry can have various singularities such as geodesic incompleteness, gauge theory quantum effects can introduce higher derivative corrections in the effective action which can serve as a way to resolve the singularities.