Chaos bound in Bershadsky-Polyakov theory

Abstract

We consider two dimensional conformal field theory (CFT) with large central charge c in an excited state obtained by the insertion of an operator Φ with large dimension Δ_Φ ∼ O(c) at spatial infinities in the thermal state. We argue that correlation functions of light operators in such a state can be viewed as thermal correlators with a rescaled effective temperature. The effective temperature controls the growth of out-of-time order (OTO) correlators and results in a violation of the universal upper bound on the associated Lyapunov exponent when Δ_Φ < 0 and the CFT is nonunitary. We present a specific realization of this situation in the holographic Chern-Simons formulation of a CFT with ${\mathrm{W}}_3^{(2)}$ symmetry also known as the Bershadsky-Polyakov algebra. We examine the precise correspondence between the semiclassical (large-c) representations of this algebra and the Chern-Simons formulation, and infer that the holographic CFT possesses a discretuum of degenerate ground states with negative conformal dimension ${\Delta}_{\Phi}=-\frac{c}{8}$. Using the Wilson line prescription to compute entanglement entropy and OTO correlators in the holographic CFT undergoing a local quench, we find the Lyapunov exponent ${\uplambda}_L=\frac{4\pi }{\beta }$_, violating the universal chaos bound.