Berlin 2024 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: AdS/CFT

MP 10.4: Talk

Thursday, March 21, 2024, 10:40–11:00, HL 001

Genus expansions and non-factorisation in periodic orbit sums: a proposal for holography in two-dimensional quantum gravity — •Fabian Haneder, Torsten Weber, Camilo Moreno, Juan Diego Urbina, and Klaus Richter — Universität Regensburg, Regensburg, Deutschland

In recent years, low dimensional quantum gravitational models have found fruitful application in holography due to dualities between such models and various random matrix models [D. Stanford, E. Witten, arXiv: 1907.03363]. An open problem in the generalisation of this work to higher dimensional quantum gravity is the question of how a single quantum system can produce non-factorising correlation functions like the ones found in random matrix models and expected in generic theories with quantum gravity due to the contribution from wormhole geometries.

In this talk, we show that generic chaotic quantum systems, after introducing a novel dynamical average utilising correlations between the actions of classical periodic orbits [M. Sieber, K. Richter, Phys. Scr. 2001 128], exhibit correlation functions that take the form of genus expansions one would expect in (2-dimensional) quantum gravity. For a specific choice of system, a particle moving geodesically on a hyperbolic 3-manifold, which is described by the mathematically exact Selberg trace formula, we find agreement to leading order in the genus expansion of the one- and two-point correlation functions of the heat kernel with the corresponding partition functions of topological 2d gravity, the gravitational dual of the Kontsevich matrix model.

Keywords: 2-dimensional gravity; Airy model; Holography; Semiclassics; Selberg Trace Formula