Pole-skipping and Rarita-Schwinger fields

TL;DR

This paper investigates pole-skipping phenomena in the equations of motion for Rarita-Schwinger fields near black hole horizons, revealing special points in Fourier space linked to chaos and holography.

Contribution

It extends the analysis of pole-skipping to Rarita-Schwinger fields, identifying special complex frequency and momentum values where solutions are regular and ingoing.

Findings

Pole-skipping points are found at specific complex frequencies and momenta.

The leading pole-skipping point relates to the Lyapunov exponent in chaotic systems.

The results connect holographic fermionic fields to chaos diagnostics.

Abstract

In this note we analyse the equations of motion of a minimally coupled Rarita-Schwinger field near the horizon of an anti-de Sitter-Schwarzschild geometry. We find that at special complex values of the frequency and momentum there exist two independent regular solutions that are ingoing at the horizon. These special points in Fourier space are associated with the `pole-skipping' phenomenon in thermal two-point functions of operators that are holographically dual to the bulk fields. We find that the leading pole-skipping point is located at a positive imaginary frequency with the distance from the origin being equal to half of the Lyapunov exponent for maximally chaotic theories.