Wheeler-DeWitt Equation in AdS/CFT Correspondence

TL;DR

This paper extends the holographic RG flow to include quantum effects via the Wheeler-DeWitt equation, enabling systematic calculation of 1/N corrections to the boundary Weyl anomaly in AdS/CFT.

Contribution

It introduces a quantum extension of the holographic RG flow using the Wheeler-DeWitt equation in AdS/CFT, capturing subleading 1/N corrections.

Findings

Agreement of 1/N^2 corrections with previous Schrödinger equation results

Reproduction of the exact boundary Weyl anomaly including KK modes

Systematic derivation of quantum corrections in holographic RG flow

Abstract

We discuss a quantum extension of the holographic RG flow equation obtained previously from the classical Hamiltonian constraint in the bulk AdS supergravity. The Wheeler-DeWitt equation is proposed to generate the extended RG flow and to produce 1/N subleading corrections systematically. Our formulation in five dimensions is applied to the derivation of the Weyl anomaly of boundary N=4 SU(N) super-Yang-Mills theory beyond the large N limit. It is shown that subleading 1/N^2 corrections arising from fields in AdS_5 supergravity agree with those obtained recently by Mansfield et al. using their Schroedinger equation, thereby guaranteeing to reproduce the exact form of the boundary Weyl anomaly after summing up all of the KK modes.