On CFT and quantum chaos

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.