# Chaos bound in Bershadsky-Polyakov theory

## TL;DR

This paper investigates chaos bounds in a specific nonunitary 2D CFT with large central charge, showing that certain excited states lead to a violation of the universal Lyapunov exponent bound, with implications for holographic duals.

## Contribution

It demonstrates how excited states in a nonunitary CFT with Bershadsky-Polyakov symmetry violate the chaos bound, linking algebraic representations to holographic chaos behavior.

## Key findings

- Correlators in excited states behave as thermal correlators with rescaled temperature.
- Violates the universal Lyapunov exponent bound in nonunitary CFT.
- Identifies a spectrum of degenerate ground states with negative conformal dimension.

## 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 \Phi with large dimension \Delta_\Phi ~ 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 \Delta_\Phi <0 and the CFT is nonunitary. We present a specific realization of this situation in the holographic Chern-Simons formulation of a CFT with {W}^{(2)}_3 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 =- 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 \lambda_L = 4\pi/ \beta, violating the universal chaos bound.