# Chaos in Three-dimensional Higher Spin Gravity

## TL;DR

This paper explores chaos in three-dimensional higher spin gravity by analyzing soft modes, eigenfunctions, and out-of-time-order correlators, revealing a Lyapunov exponent that scales with the spin number.

## Contribution

It derives the higher spin generalization of the Schwarzian action, computes soft mode eigenfunctions, and evaluates chaos indicators in $SL(N)$ higher spin gravity.

## Key findings

- Lyapunov exponent scales as ${2 ext{ extpi}}/{eta}(N-1)$
- Derived higher spin Schwarzian on-shell action
- Computed soft mode eigenfunctions from $ ext{ extW}$-Ward identities

## Abstract

We discuss $SL(N,\mathbb{C})$ Chern-Simons higher spin gauge theories in Euclidean AdS$_3$. With appropriate boundary term, we derive the higher spin generalization of Schwarzian on-shell action. We investigate gravitationally dressed bi-locals, and we study the soft higher spin mode expansion to obtain soft mode eigenfunctions. We also derive the spin-$s$ eigenfunction from $\mathcal{W}$-Ward identity and a recursion relation. Using the on-shell action, we evaluate the contributions of the soft higher spin modes to the out-of-time-order correlators, and the corresponding Lyapunov exponent of $SL(N)$ higher spin gravity is found to be ${2\pi \over \beta}(N-1)$.