SMuK 2023 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: AdS/CFT Correspondence II

MP 10.1: Talk

Thursday, March 23, 2023, 14:00–14:20, ZEU/0250

Towards a Quantum Chaotic Dual of JT Gravity — •Fabian Haneder, Torsten Weber, Camilo Moreno, Juan Diego Urbina, and Klaus Richter — Universität Regensburg, Deutschland

Jackiw-Teitelboim (JT) quantum gravity is a two-dimensional model that has received a striking amount of attention in recent years as a simple example of holography, given its duality to the low-energy regime of the SYK model, as well as full perturbative equivalence to a matrix model found by Saad, Shenker and Stanford. We take first steps towards establishing a further duality between JT gravity and the chaotic quantum dynamics of a particle on a high dimensional compact manifold of constant negative curvature. The presence of a single system, instead of an ensemble, on the non-gravitational side of the duality allows us to identify possible degrees of freedom and corresponding mechanisms responsible for the quantum-chaotic features in JT gravity. We address key aspects of JT correlation functions by showing how the Schwarzian density of states, which bridges quantum gravity and disordered systems, such as SYK, is identical to the Weyl (smooth) term of the Selberg trace formula describing exactly the quantum spectrum on the compact manifold. Time permitting, we use periodic orbit theory to derive an effective trace formula over coarse-grained bundles of geodesics, and show that it admits a genus expansion structurally identical to the JT correlators.