Radial canonical AdS 3 gravity and T T ¯

Journal article

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 TT¯ theory as a Schrödinger wavefunctional satisfying a Schrödinger evolution equation in volume time, and the TT¯ 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 TT¯ interpretation, as well as semi-classical Wheeler-DeWitt states for that solution.

Authors: Blacker, MJ; Callebaut, N; Hergueta, B; Ning, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2025
• Issue: 1
• Article number: 92
• Publication date: 2025-01-17
• Acceptance date: 2024-12-16
• DOI: 10.1007/jhep01(2025)092
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: Classical Theories of Gravity; Field Theories in Lower Dimensions; AdS-CFT Correspondence; Gauge-Gravity Correspondence