Spectral form factor in the $\tau$-scaling limit

TL;DR

This paper develops a systematic method to compute higher order corrections to the spectral form factor in topological gravity within the tau-scaling limit, providing explicit results and insights into the structure of these corrections.

Contribution

It introduces a technique for calculating higher order corrections to the spectral form factor in the tau-scaling limit of topological gravity, with explicit formulas for several cases.

Findings

Derived the first five corrections to the SFF in closed form.

Connected higher order corrections to Fourier transforms of sine-kernel modifications.

Applied the method to Airy and JT gravity examples.

Abstract

We study the spectral form factor (SFF) of general topological gravity in the limit of large time and fixed temperature. It has been observed recently that in this limit, called the tau-scaling limit, the genus expansion of the SFF can be summed up and the late-time behavior of the SFF such as the ramp-plateau transition can be studied analytically. In this paper we develop a technique for the systematic computation of the higher order corrections to the SFF in the strict tau-scaling limit. We obtain the first five corrections in a closed form for the general background of topological gravity. As concrete examples, we present the results for the Airy case and Jackiw-Teitelboim gravity. We find that the above higher order corrections are the Fourier transforms of the corrections to the sine-kernel approximation of the Christoffel-Darboux kernel in the dual double-scaled matrix integral, which naturally explains their structure. Along the way we also develop a technique for the systematic computation of the corrections to the sine-kernel formula, which have not been fully explored in the literature before.