Unorientable topological gravity and orthogonal random matrix universality

TL;DR

This paper demonstrates that unorientable topological gravity exhibits universal quantum chaos signatures, aligning with orthogonal random matrix theory, through analysis of spectral form factors and Weil-Petersson volumes, extending chaos-gravity duality.

Contribution

It extends the gravity/chaos duality to unorientable manifolds by analyzing the Airy model and deriving universal chaos signatures in unorientable topological gravity.

Findings

Universal signatures of quantum chaos are observed in unorientable JT gravity.

The spectral form factor shows agreement with orthogonal RMT after regularization.

Weil-Petersson volumes for unorientable geometries are computed and used to support results.

Abstract

The duality of Jackiw-Teitelboim (JT) gravity and a double scaled matrix integral has led to studies of the canonical spectral form factor (SFF) in the so called $\tau-$scaled limit of large times, $t \to \infty$, and fixed temperature in order to demonstrate agreement with universal random matrix theory (RMT). Though this has been established for the unitary case, extensions to other symmetry classes requires the inclusion of unorientable manifolds in the sum over geometries, necessary to address time reversal invariance, and regularization of the corresponding prime geometrical objects, the Weil-Petersson (WP) volumes. We report here how universal signatures of quantum chaos, witnessed by the fidelity to the Gaussian orthogonal ensemble, emerge for the low-energy limit of unorientable JT gravity, i.e. the Airy model/topological gravity. To this end, we implement the loop equations for the corresponding dual (double-scaled) matrix model and find the generic form of the Airy WP volumes, supported by calculations using unorientable Kontsevich graphs. In an apparent violation of the gravity/chaos duality, the $\tau-$scaled SFF on the gravity side acquires both logarithmic and power law contributions in $t$, not manifestly present on the RMT side. We show the expressions can be made to agree by means of bootstrapping-like relations hidden in the asymptotic expansions of generalized hypergeometric functions. Thus, we are able to establish strong evidence of the quantum chaotic nature of unorientable topological gravity.