A bound on chaos from stability

Abstract

Abstract We explore the quantum chaos of the coadjoint orbit action of diffeomorphism group of S 1. 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(S 1)/SL(2) while the other stable orbit Diff(S 1)/U(1) where the SL(2, ℝ) is broken to U(1) has non-maximal Lyapunov exponent.

Keywords

• 2D Gravity
• AdS-CFT Correspondence
• Field Theories in Lower Dimensions