Setting the boundary free in AdS/CFT

We describe a new class of boundary conditions for AdSd+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.