Finite Cutoff AdS$_{5}$ Holography and the Generalized Gradient Flow

TL;DR

This paper explores how double trace deformations in four-dimensional large N holographic CFTs relate to finite radius hypersurfaces in the bulk, revealing a generalized gradient flow structure in the induced gravity theory.

Contribution

It establishes a variable transformation linking deformation equations to the bulk radial ADM Hamiltonian, clarifies the role of background functions, and introduces a generalized gradient flow perspective.

Findings

Transformation connects deformation equations to bulk Hamiltonian.

Deformations induce a generalized gradient flow in the induced gravity.

Flow potential matches the two-derivative effective action from holographic renormalization.

Abstract

Recently proposed double trace deformations of large $N$ holographic CFTs in four dimensions define a one parameter family of quantum field theories, which are interpreted in the bulk dual as living on successive finite radius hypersurfaces. The transformation of variables that turns the equation defining the deformation of a four dimensional large $N$ CFT by such operators into the expression for the radial ADM Hamiltonian in the bulk is found. This prescription clarifies the role of various functions of background fields that appear in the flow equation defining the deformed holographic CFT, and also their relationship to the holographic anomaly. The effect of these deformations can also be seen as triggering a generalized gradient flow for the fields of the induced gravity theory obtained from integrating out the fundamental fields of the holographic CFT. The potential for this gradient flow is found to resemble the two derivative effective action previously derived using holographic renormalization.