Chaos bound in Bershadsky-Polyakov theory

Abstract

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 ΔΦ ∼ 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 ΔΦ < 0 and the CFT is nonunitary. We present a specific realization of this situation in the holographic Chern-Simons formulation of a CFT with $$ {\mathrm{W}}_3^{(2)} $$ 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 $$ {\Delta}_{\Phi}=-\frac{c}{8} $$ Δ Φ = − 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 $$ {\uplambda}_L=\frac{4\pi }{\beta } $$ λ L = 4 π β , violating the universal chaos bound.