Setting the boundary free in AdS/CFT

TL;DR

This paper introduces a new class of boundary conditions in AdS/CFT where the boundary metric becomes dynamical, allowing for novel couplings between conformal field theories and gravity, with implications for stability and boundary dynamics.

Contribution

It presents boundary conditions that make the boundary metric dynamical in AdS/CFT, extending the framework to include coupled CFT and gravity theories with stable configurations.

Findings

Boundary counter-terms render boundary metric fluctuations normalizable.

Neumann boundary conditions promote the CFT metric to a dynamical field without explicit gravity.

Coupling topologically massive gravity to a large N CFT remains perturbatively stable.

Abstract

We describe a new class of boundary conditions for AdS_{d+1} under which the boundary metric becomes a dynamical field. The key technical point is to show that contributions from boundary counter-terms in the bulk gravitational action render such fluctuations normalizable. In the context of AdS/CFT, the analogue of Neumann boundary conditions for AdS promotes the CFT metric to a dynamical field but adds no explicit gravitational dynamics; the gravitational dynamics is just that induced by the conformal fields. Other AdS boundary conditions couple the CFT to a gravity theory of choice. We use this correspondence to briefly explore the coupled CFT + gravity theories and, in particular, for d=3 we show that coupling topologically massive gravity to a large N CFT preserves the perturbative stability of the theory with negative (3-dimensional) Newton's constant.