# Eigenvalue instantons in the spectral form factor of random matrix model

## TL;DR

This paper investigates the late-time behavior of the spectral form factor in GUE random matrices, revealing non-perturbative eigenvalue instanton effects that cause deviations from a perfect plateau.

## Contribution

It introduces the concept of eigenvalue instantons as a source of non-perturbative corrections in the spectral form factor of random matrix models.

## Key findings

- Eigenvalue instantons contribute to the spectral form factor plateau.
- Non-zero time derivative due to instantons is explicitly computed.
- Instanton effects are significant in understanding late-time spectral behavior.

## Abstract

We study the late time plateau behavior of the spectral form factor in the Gaussian Unitary Ensemble (GUE) random matrix model. The time derivative of the spectral form factor in the plateau regime is not strictly zero, but non-zero due to a non-perturbative correction in the $1/N$ expansion. We argue that such a non-perturbative correction comes from the eigenvalue instanton of random matrix model and we explicitly compute the instanton correction as a function of time.