Pole skipping in holographic theories with gauge and fermionic fields

TL;DR

This paper extends the pole-skipping formalism in holographic theories to include gauge fields and fermions, providing a unified approach to identify special frequencies related to the highest spins in the theory.

Contribution

It introduces a gauge-invariant formalism for pole skipping and incorporates fermionic fields with various spins, broadening the applicability of the method.

Findings

Pole-skipping points are identified at frequencies related to the highest spins.

The formalism works without gauge redundancy removal.

Examples demonstrate the practical application across different spins.

Abstract

Using covariant expansions, recent work showed that pole skipping happens in general holographic theories with bosonic fields at frequencies $\mathrm{i}(l_b-s) 2\pi T$, where $l_b$ is the highest integer spin in the theory and $s$ takes all positive integer values. We revisit this formalism in theories with gauge symmetry and upgrade the pole-skipping condition so that it works without having to remove the gauge redundancy. We also extend the formalism by incorporating fermions with general spins and interactions and show that their presence generally leads to a separate tower of pole-skipping points at frequencies $\mathrm{i}(l_f-s)2\pi T$, $l_f$ being the highest half-integer spin in the theory and $s$ again taking all positive integer values. We also demonstrate the practical value of this formalism using a selection of examples with spins $0,\frac{1}{2},1,\frac{3}{2},2$.