Abstract
We explore the quantum chaos of the coadjoint orbit action of diffeomorphism group of S1. We study quantum fluctuation around a saddle point to evaluate the soft mode contribution to the out-of-time-ordered correlator. We show that the stability condition of the semi-classical analysis of the coadjoint orbit found in [1] leads to the upper bound on the Lyapunov exponent which is identical to the bound on chaos proven in [2]. The bound is saturated by the coadjoint orbit Diff(S1)/SL(2) while the other stable orbit Diff(S1)/U(1) where the SL(2, ℝ) is broken to U(1) has non-maximal Lyapunov exponent.
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Yoon, J. A bound on chaos from stability. J. High Energ. Phys. 2021, 97 (2021). https://doi.org/10.1007/JHEP11(2021)097
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DOI: https://doi.org/10.1007/JHEP11(2021)097