TL;DR
This paper explores the connection between conformal field theories and quantum chaos, showing that certain 1+1-D systems exhibit chaos characteristics and linking their spectra to black hole quasi-normal modes.
Contribution
It identifies chaos features in 1+1-D CFTs with non-linear conformal symmetry and constructs a lattice model using parafermionic spins to study quantum chaos.
Findings
CFTs with non-linear conformal symmetry show maximal Lyapunov behavior.
The spectrum of Ruelle resonances in these CFTs matches black hole quasi-normal modes.
A lattice model based on parafermionic spins demonstrates quantum chaos properties.
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.
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