Radial canonical AdS3 gravity and T T ¯ $$ T\overline{T} $$ - Matthew J. Blacker; Nele Callebaut; Blanca Hergueta; Sirui Ning (Journal of High Energy Physics)
Abstract We employ an ADM deparametrization strategy to discuss the radial canonical formalism of asymptotically AdS3 gravity. It leads to the identification of a radial ‘time’ before quantization, which is the volume time, canonically conjugate to York time. Holographically, this allows to interpret the semi-classical path integral of T T ¯ $$ T\overline{T} $$ theory as a Schrödinger wavefunctional satisfying a Schrödinger evolution equation in volume time, and the T T ¯ $$ T\overline{T} $$ operator expectation value in terms of the Hamiltonian that generates volume time translations — both consistent with cut-off holography. We make use of the canonical perspective to construct the rotating BTZ solution from the Hamilton-Jacobi equation, with a finite cut-off energy spectrum that has a known holographic T T ¯ $$ T\overline{T} $$ interpretation, as well as semi-classical Wheeler-DeWitt states for that solution.