Type: Article
Publication Date: 2019-07-01
Citations: 16
DOI: https://doi.org/10.1007/jhep07(2019)046
A bstract We discuss SL( N, 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 Ward identity of $$ \mathcal{W} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>W</mml:mi> </mml:math> -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 $$ \frac{2\pi }{\beta}\left(N - 1\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> <mml:mi>β</mml:mi> </mml:mfrac> <mml:mfenced> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mspace /> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> .