Higher curvature corrections to pole-skipping

TL;DR

This work shows that higher-curvature corrections from stringy $R^4$ and Gauss-Bonnet $R^2$ terms do not alter the pole-skipping frequencies $\omega_n=-i2\pi Tn$ in holographic retarded correlators, but they do shift the corresponding momenta $k_n$ in a spin-dependent and correction-dependent manner. Using a systematic near-horizon expansion, the authors compute the corrections to $k_n$ for scalar, vector, and metric perturbations across the lower-half complex-frequency plane, revealing robust universality of the imaginary frequency set by temperature while exposing the sensitivity of dispersion data to finite-coupling effects. The upper-half-plane (chaos-related) pole-skipping point is recovered, and within the sound channel, yields consistent chaos parameters such as the Lyapunov exponent $\lambda_L=2\pi T$ and a corrected butterfly velocity $v_B$ under higher-curvature corrections. The findings reinforce the view that pole-skipping encodes universal near-horizon physics that governs both chaos and hydrodynamic constraints, with higher-curvature corrections providing controlled probes of finite coupling effects in strongly coupled plasmas.

Abstract

Recent developments have revealed a new phenomenon, i.e. the residues of the poles of the holographic retarded two point functions of generic operators vanish at certain complex values of the frequency and momentum. This so-called pole-skipping phenomenon can be determined holographically by the near horizon dynamics of the bulk equations of the corresponding fields. In particular, the pole-skipping point in the upper half plane of complex frequency has been shown to be closed related to many-body chaos, while those in the lower half plane also places universal and nontrivial constraints on the two point functions. In this paper, we study the effect of higher curvature corrections, i.e. the stringy correction and Gauss-Bonnet correction, to the (lower half plane) pole-skipping phenomenon for generic scalar, vector, and metric perturbations. We find that at the pole-skipping points, the frequencies $ω_n=-i2πnT$ are not explicitly influenced by both $R^2$ and $R^4$ corrections, while the momenta $k_n$ receive corresponding corrections.