Setting the boundary free in AdS/CFT

TL;DR

The authors introduce a Neumann boundary condition framework in AdS/CFT that makes the boundary metric dynamical, interpreting the bulk path integral as a CFT coupled to induced gravity on the boundary. By including boundary counterterms, they show the leading Fefferman–Graham mode fluctuations are normalizable and that the total symplectic structure is conserved under these boundary conditions. They analyze conserved charges and gauge structure across Dirichlet, Neumann, and mixed setups, demonstrating that boundary diffeomorphisms (and Weyl transformations for odd dimensions) act as gauge symmetries in the Neumann/mixed cases. In particular, the linearized boundary dynamics is ghost- and tachyon-free for odd $d$ (with $d=3$ allowing interesting TMG-like deformations), while even $d$ exhibits tachyonic/ghost modes; the $d=2$ case reduces to Liouville-like boundary gravity, providing a UV-complete, holographic setting for CFTs coupled to boundary gravity and suggesting several future extensions and UV completions.

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.