Speaker
Description
We discuss the radial canonical formalism for asymptotically AdS$_3$ gravity. We employ an ADM deparametrization procedure that allows the identification of a preferred 'time' before quantization, the volume time, which is canonically conjugate to York time. This leads to the identification of the (radial) Wheeler-DeWitt (WdW) equation with the Schr\"odinger equation in volume time. In the context of holography, the WdW equation is interpreted as the flow generated by the $T\bar{T}$ deformation of a 2-dimensional CFT living on the conformal boundary of AdS$_3$. Unlike previous works, we discuss this duality using the natural language provided by the volume time identification.
Later we make this duality explicit by applying the radial canonical formalism to a concrete example: the BTZ black hole, where we find the correspondence between the conserved charges and the $T\bar{T}$ spectrum.
This talk will be based on 2406.02508, with M. Blacker., N. Callebaut and S. Ning.
