A late times approximation for the SYK spectral form factor

TL;DR

This paper develops a late-time approximation for the SYK spectral form factor using a large N steepest descent approach, involving spectral analysis and regularization techniques.

Contribution

It introduces a novel large N steepest descent method to approximate the SYK spectral form factor at late times, incorporating spectral analysis and regularization.

Findings

Derived a late-time approximation for the spectral form factor.

Identified key spectral properties of the two replica ladder kernel.

Established a regularization scheme for the kinetic operator.

Abstract

We find a late times approximation for the SYK spectral form factor from a large $N$ steepest descent version of the path integral over two replica collective fields. Main ingredients are a suitable uv regularization of the two replica kinetic operator, the property of its Fourier transform and some spectral analysis of the four point function two replica ladder kernel.