Higher-spin localized shocks

TL;DR

This work extends the holographic chaos/OTOC framework to theories with isolated higher-spin fields by constructing exact localized shockwave solutions on AdS black hole backgrounds for spins $\ell\ge2$. Using a worldline coupling, it computes the OTOC and shows the Lyapunov exponent is $\lambda_L=(\ell-1)\,2\pi T$ with a butterfly velocity $v_B$ set by the shockwave profile; for $\ell\ge3$ this exponent can violate the chaos bound and the butterfly velocity can exceed light speed, indicating potential boundary causality issues. The analysis connects shockwaves to pole skipping, identifying the leading pole-skipping point as $\omega=i\lambda_L$ and $k=i\lambda_L/v_B$, and shows the high-spin shockwave corresponds to a quasinormal mode at this special point. Time-delay versus time-machine behavior is examined via probe-worldline couplings, revealing causality constraints that depend on the sign of kinetic terms and the high-spin content. Overall, the paper demonstrates that higher-spin bulk dynamics imprint sharp, universal signatures on boundary chaos diagnostics and highlights fundamental constraints on consistent higher-spin holography.

Abstract

In the context of AdS/CFT, gravitational shockwaves serve as a geometric manifestation of boundary quantum chaos. We study this connection in general diffeomorphism-invariant theories involving an arbitrary number of bosonic fields. Specifically, we demonstrate that theories containing spin-2 or higher-spin fields generally admit classical localized shockwave solutions on black hole backgrounds, whereas spin-0 and spin-1 theories do not. As in the gravitational case, these higher-spin shockwaves provide a means to compute the out-of-time-order correlator. Both the Lyapunov exponent and the butterfly velocity are found to universally agree with predictions from pole skipping. In particular, higher-spin fields lead to a Lyapunov exponent that violates the chaos bound and a butterfly velocity that may exceed the speed of light.