Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT

TL;DR

This paper systematically studies multi-trace deformations in AdS/CFT, revealing their effects on vacuum structure, providing new solutions, and establishing a method to compute the holographic effective action.

Contribution

It introduces a comprehensive approach to analyze multi-trace deformations in AdS/CFT, including new analytic solutions and a Hamilton-Jacobi based method for effective action calculation.

Findings

Supergravity solutions correspond to critical points of the holographic effective action.

New exact analytic solutions involving scalar fields with mixed boundary conditions.

A systematic Hamilton-Jacobi method for computing the holographic effective action.

Abstract

We present a general and systematic treatment of multi-trace deformations in the AdS/CFT correspondence in the large N limit, pointing out and clarifying subtleties relating to the formulation of the boundary value problem on a conformal boundary. We then apply this method to study multi-trace deformations in the presence of a scalar VEV, which requires the coupling to gravity to be taken into account. We show that supergravity solutions subject to `mixed' boundary conditions are in one-to-one correspondence with critical points of the holographic effective action of the dual theory in the presence of a multi-trace deformation, and we find a number of new exact analytic solutions involving a minimally or conformally coupled scalar field satisfying `mixed' boundary conditions. These include the generalization to any dimension of the instanton solution recently found in hep-th/0611315. Finally, we provide a systematic method for computing the holographic effective action in the presence of a multi-trace deformation in a derivative expansion away from the conformal vacuum using Hamilton-Jacobi theory. Requiring that this effective action exists and is bounded from below reproduces recent results on the stability of the AdS vacuum in the presence of `mixed' boundary conditions.