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arXiv · 2406.02508

Radial canonical AdS$_3$ gravity and $T\bar{T}$

Matthew J. Blacker·Nele Callebaut·Blanca Hergueta·Sirui Ning
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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 $T\bar T$ theory as a Schr\"odinger wavefunctional satisfying a Schr\"odinger evolution equation in volume time, and the $T\bar T$ 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 $T\bar T$ interpretation, as well as semi-classical Wheeler-DeWitt states for that solution.

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Matthew J. Blacker, Nele Callebaut, Blanca Hergueta, Sirui Ning. 2024-06-04. Radial canonical AdS$_3$ gravity and $T\bar{T}$. https://arxiv.org/abs/2406.02508

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