Pole skipping in holographic theories with bosonic fields

TL;DR

This paper investigates pole skipping phenomena in holographic conformal field theories with bosonic fields, revealing how higher spin fields influence chaos-related quantities and establishing connections with shockwave calculations.

Contribution

It derives general pole-skipping conditions in holographic theories with bosonic fields and elucidates the role of higher spin fields in chaos and energy density correlators.

Findings

Higher spin fields lead to a higher-weight pole-skipping point with a Lyapunov exponent outside the chaos bound.

Without higher spin fields, the energy density Green's function's pole skipping matches the chaos bound and shockwave velocity.

The paper provides a metric-level explanation for the matching between pole skipping and chaos parameters.

Abstract

We study pole skipping in holographic CFTs dual to diffeomorphism invariant theories containing an arbitrary number of bosonic fields in the large $N$ limit. Defining a weight to organize the bulk equations of motion, a set of general pole-skipping conditions are derived. In particular, the frequencies simply follow from general covariance and weight matching. In the presence of higher spin fields, we find that the imaginary frequency for the highest-weight pole-skipping point equals the higher-spin Lyapunov exponent which lies outside of the chaos bound. Without higher spin fields, we show that the energy density Green's function has its highest-weight pole skipping happening at a location related to the OTOC for arbitrary higher-derivative gravity, with a Lyapunov exponent saturating the chaos bound and a butterfly velocity matching that extracted from a shockwave calculation. We also suggest an explanation for this matching at the metric level by obtaining the on-shell shockwave solution from a regularized limit of the metric perturbation at the skipped pole.