Pole-skipping with finite-coupling corrections

TL;DR

The paper investigates finite-coupling (α') corrections to pole-skipping in holography by analyzing higher-derivative corrections in both pure gravity and Einstein–Maxwell theories. It shows that the Matsubara-like frequencies ω_n are universal and remain unshifted to leading order, while the corresponding wave numbers q_n receive coupling-dependent shifts, with some special points disappearing at particular couplings. Through the Gauss–Bonnet and Weyl-type corrections, the work elucidates how higher-derivative terms modify the pole-skipping structure, the role of field redefinitions, and the interplay with electromagnetic duality in 4D Maxwell theory. The results highlight a robust ω_n = -i n pattern across several perturbations, while revealing selective sensitivity of q_n and the possible nonperturbative disappearance of certain special points within causality bounds. These findings deepen understanding of Green’s-function nonuniqueness in strongly coupled systems and its relation to chaos, dualities, and universal hydrodynamic features.

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 $ω_n = -(2πT)ni$ 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 $ω_n$ 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.