Radial canonical AdS$_3$ gravity and $T\bar{T}$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910889023635456 |
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| author | Blacker, Matthew J. Callebaut, Nele Hergueta, Blanca Ning, Sirui |
| author_facet | Blacker, Matthew J. Callebaut, Nele Hergueta, Blanca Ning, Sirui |
| contents | 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 Schrödinger wavefunctional satisfying a Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Radial canonical AdS$_3$ gravity and $T\bar{T}$ Blacker, Matthew J. Callebaut, Nele Hergueta, Blanca Ning, Sirui High Energy Physics - Theory 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 Schrödinger wavefunctional satisfying a Schrödinger 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. |
| title | Radial canonical AdS$_3$ gravity and $T\bar{T}$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.02508 |