Pole-skipping with finite-coupling corrections

TL;DR

This paper investigates how finite-coupling corrections affect pole-skipping points in holographic Green's functions, revealing that while frequencies remain unchanged, wave numbers are corrected and some points may vanish.

Contribution

It provides the first analysis of finite-coupling effects on pole-skipping points, showing corrections to wave numbers and the disappearance of some special points at specific couplings.

Findings

Wave numbers are corrected at finite coupling.

Some pole-skipping points disappear at certain higher-derivative couplings.

Maxwell scalar and vector modes are related by electromagnetic duality.

Abstract

Recently, it is shown that many Green's functions are not unique at special points in complex momentum space using AdS/CFT. This phenomenon is similar to the pole-skipping in holographic chaos, and the special points are typically located at $\omega_n = -(2\pi T)ni$ with appropriate values of complex wave number $q_n$. We study finite-coupling corrections to special points. As examples, we consider four-derivative corrections to gravitational perturbations and four-dimensional Maxwell perturbations. While $\omega_n$ is uncorrected, $q_n$ is corrected at finite coupling. Some special points disappear at particular values of higher-derivative couplings. Special point locations of the Maxwell scalar and vector modes are related to each other by the electromagnetic duality.