Chaos in three-dimensional higher spin gravity

Abstract

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 \( \mathcal{W} \)-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 \( \frac{2\pi }{\beta}\left(N - 1\right) \).

A preprint version of the article is available at ArXiv.

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Narayan, P., Yoon, J. Chaos in three-dimensional higher spin gravity. J. High Energ. Phys. 2019, 46 (2019). https://doi.org/10.1007/JHEP07(2019)046

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Keywords

  • AdS-CFT Correspondence
  • Black Holes
  • Conformal and W Symmetry
  • Higher Spin Gravity