Juan-Diego Urbina

Low-dimensional quantum gravity is chaotic: what (maybe) do quantum chaos and periodic orbit theory have to say

During the last decade, a new paradigm has emerged where the quantum-chaotic aspects of both realistic and toy-like models of quantum gravity play a fundamental role. In the case of our 3+1 dimensional universe, a celebrated aspect of this picture is the consistent idea of black holes as fast, in fact the fastest, scramblers.

Research on the quantum signatures of chaos in gravitational models got then a very strong input from the study of solvable models in low (1+1) dimensions, specially after the celebrated paper of Saad, Shenker and Stanford in 2019 where Jackiw-Teitelboim (a particularly simple model of two-dimensional quantum gravity) was shown to be dual to a matrix theory in the precise sense that the genus expansions of their spectral correlators can be shown to be identical. In particular SSS shows that JT gravity posses an universal limit of its spectral correlators given by Random Matrix Theory: JT gravity displays quantum chaos.

This remarkable result opens the door to ask whether quantum gravitational degrees of freedom can be interpreted as having a classical chaotic limit, where techniques and ideas from semiclassical analysis, in particular Gutzwiller trace formula and its versions, can be invoked to explain the emergence of such universal spectral fluctuations. In this direction, a first step is to establish a semiclassical mechanism for the emergence of genus expansions of semiclassically-calculated spectral correlators.

In this talk, I present an introduction to the main ideas behind the JT/RMT duality from the quantum chaos perspective, and then I will explain the efforts currently undergoing in our group in Regensburg to connect the corresponding results from suitable defined semiclassical correlators of an underlying classical theory displaying classical chaos. I will make special emphasis on the several open questions and possible directions to pursue within the general moto of quantum gravitational chaos as signature of classical chaos.

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/fb6ba0972c0149f096c1c4df7602c0bf1d