3D Gravity in a Box

Understand

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 $T \overline{T}$-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 $T\overline{T}$-deformed holographic CFT.