On CFT and quantum chaos
Gustavo Turiaci (Physics Department, Princeton University, Princeton, NJ, 08544, U.S.A.); Herman Verlinde (Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, 08544, U.S.A., Physics Department, Princeton University, Princeton, NJ, 08544, U.S.A.)
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.