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

TL;DR

The paper develops a time-dependent AdS/CFT framework in which the boundary ${N}=4$ SYM is reformulated on a flat base with time-dependent couplings, enabling a perturbative analysis. By computing the 1-loop Wilsonian effective action and applying a holographic UV/IR relation, the authors show how the bulk metric can be reconstructed from boundary data, with the fermion kinetic term encoding the bulk $g_{++}$ component and higher-loop corrections yielding a full 5D metric. They argue that gauge-theory quantum corrections generate higher-derivative terms that smear geometry at the cutoff scale, providing a mechanism to resolve null singularities such as $R_{++}$ divergences. The work establishes a concrete link between boundary quantum dynamics and bulk geometry, and points to extensions involving axion dynamics, SL(2,Z) duality, and higher-order gravity corrections.

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.

Figures (2)

• Figure 1: One-loop contribution to the fermion kinetic term from gauge boson and scalars
• Figure 2: Contribution due to propagator corrections