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Title:
Quantum Jackiw-Teitelboim gravity and Random Matrix Theory
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Abstract:
We show that the spectrum of quantum Jackiw-Teitelboim (JT) gravity is equivalent to the spectrum of a Maass form on a Riemann surfaces of genus $g\geq 2$ and infinite area. The resulting spectrum is semiclasically exact and closely related to a Selberg trace formula, namely, it is expressed as a sum over the closed geodesics of a compact Riemann surface of genus g. By using semiclassical techniques, we compute analytically the spectral form factor and find agreement with random matrix theory for sufficiently long times. This shows that quantum ergodicity is a distinct feature of JT quantum gravity.
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