Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
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.
Cite
@article{arxiv.hep-th/0602106,
title = {Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT},
author = {Thomas Hartman and Leonardo Rastelli},
journal= {arXiv preprint arXiv:hep-th/0602106},
year = {2008}
}
Comments
30 pages, LaTex. v2: reference added