Pole skipping in holographic theories with gauge and fermionic fields

TL;DR

The paper develops a comprehensive pole-skipping framework for holographic theories with bosonic, gauge, and fermionic bulk fields. It introduces a gauge-covariant formulation that avoids gauge-fixing and extends the covariant expansion to fermions, revealing universal pole-skipping towers at frequencies $ω=i(l_b-s)2πT$ for bosons and $ω=i(l_f-s)2πT$ for fermions, with two towers coexisting when both types are dynamical. The authors provide practical algorithms and several example treatments across spins $0,1/2,1,3/2,2$, and outline how mixed boson–fermion systems naturally yield dual towers, potentially linking to chaos via OTOCs. They discuss limitations (infinite-matrix inversions) and avenues for extension, including rotating backgrounds and non-black-hole geometries, highlighting the broad applicability of the covariant approach to constrain quasinormal-mode spectra. These results deepen the understanding of the analytic structure of holographic Green's functions and their chaotic properties in richly structured bulk theories.

Abstract

Using covariant expansions, recent work showed that pole skipping happens in general holographic theories with bosonic fields at frequencies $\mathrm{i}(l_b-s) 2πT$, 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 $\mathrm{i}(l_f-s)2πT$, $l_f$ 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 $0,\frac{1}{2},1,\frac{3}{2},2$.