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On CFT and Quantum Chaos

Abstract

We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.Comment: 26 pages, 2 figures. References adde

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