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Two-dimensional quantum gravity and many-body quantum chaos
Dissertation

Two-dimensional quantum gravity and many-body quantum chaos

Jarod Tall
Doctor of Philosophy (PhD), Washington State University
2026
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Open Access CC BY V4.0

Abstract

Random matrix theory has been used with incredible success to provide a statistical theory for the spectral fluctuations of quantum chaotic Hamiltonians. In recent years, there has been growing evidence that quantum gravitational theories are quantum chaotic, and thus random matrix theory is applicable. In two-dimensional quantum gravity, this statement can be made very precise. Jackiw-Teitelboim (JT) gravity is a simple theory of gravity in two spacetime dimensions that can be quantized directly via the Euclidean gravitational path integral. The path integral maps directly to a special type of matrix model which provides the connection to quantum chaos. It is necessary to specify whether or not JT gravity is being considered on orientable or unorientable surfaces, and this changes the symmetry class of the matrix model. In this thesis, we consider unorientable JT gravity and develop methods to solve the dual matrix model. This allows us to compute the spectral form factor of unorientable JT gravity and compare the result to universal random matrix theory. The Sachdev-Ye-Kitaev (SYK) model is a quantum chaotic model with the same low energy effective action as JT gravity. We show a similar class of models, known as embedded ensembles, exhibit the same behavior and are also solvable in the double-scaled limit. We develop new techniques to solve the density of states and $n$-point functions of double-scaled models.

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