3D gravity in a box

The quantization of pure 3D gravity with Dirichlet boundary conditions on a finite boundary is of interest both as a model of quantum gravity in which one can compute quantities which are more local than S-matrices or asymptotic boundary correlators, and for its proposed holographic duality to T (T) over bar -deformed CFTs. In this work we apply covariant phase space methods to deduce the Poisson bracket algebra of boundary observables. The result is a one-parameter nonlinear deformation of the usual Virasoro algebra of asymptotically AdS(3) gravity. This algebra should be obeyed by the stress tensor in any T (T) over bar -deformed holographic CFT. We next initiate quantization of this system within the general framework of coadjoint orbits, obtaining - in perturbation theory - a deformed version of the Alekseev-Shatashvili symplectic form and its associated geometric action. The resulting energy spectrum is consistent with the expected spectrum of T (T) over bar -deformed theories, although we only carry out the explicit comparison to O(1/root c) in the 1/c expansion.

Automated summary

The quantization process of 3D gravity with Dirichlet boundary conditions on a finite boundary is explored, resulting in a one-parameter nonlinear deformation of the Virasoro algebra. This deformed algebra is expected to be followed by the stress tensor in any T (T) over bar -deformed holographic CFT. The energy spectrum obtained through quantization is consistent with the expected spectrum of T (T) over bar -deformed theories.