Radial canonical AdS_3 gravity and TT̅
arxiv(2024)
Abstract
We employ an ADM deparametrization strategy to discuss the radial canonical
formalism of asymptotically AdS_3 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 TT̅ theory as a Schrödinger
wavefunctional satisfying a Schrödinger evolution equation in volume time,
and the TT̅ 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 TT̅ interpretation, as well as semi-classical
Wheeler-DeWitt states for that solution.
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