Chaos in three-dimensional higher spin gravity

We discuss SL(N, ℂ) Chern-Simons higher spin gauge theories in Euclidean AdS₃. 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 Ward identity of $W$-algebra 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 $\frac{2\pi }{\beta }(N-1)$.