Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT

TL;DR

This paper explores how double-trace deformations in boundary theories correspond to mixed boundary conditions in the bulk AdS space, analyzing their effects on central charges and correlators through functional determinants.

Contribution

It provides a unified explanation for the universal agreement of central charge differences and clarifies the computation of correlators with mixed boundary conditions in AdS/CFT.

Findings

The change in central charge matches exactly in bulk and boundary calculations.

A simple kinematic explanation for the universal agreement of central charges is provided.

Clarification of the prescription for computing correlators with Delta_- boundary conditions.

Abstract

According to the AdS/CFT dictionary, perturbing the large N boundary theory by a relevant double-trace deformation of the form f O^2 corresponds in the bulk to imposing ``mixed'' boundary conditions for the field dual to O. In this note we address various aspects of this correspondence. The change c_{UV} - c_{IR} of the central charge between the UV ad IR fixed points is known from explicit calculations (hep-th/0210093, hep-th/0212138) to be exactly the same in the bulk and in the boundary theories. By comparing the appropriate bulk and boundary functional determinants, we give a simple ``kinematic'' explanation for this universal agreement. We also clarify the prescription for computing AdS/CFT correlators with Delta_- boundary conditions.