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Chaos bound in Bershadsky-Polyakov theory

Justin R. David, Timothy J. Hollowood, Surbhi Khetrapal, Prem Kumar Orcid Logo

Journal of High Energy Physics, Volume: 2019, Issue: 10

Swansea University Author: Prem Kumar Orcid Logo

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DOI (Published version): 10.1007/jhep10(2019)077

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∆ ∼ O(c) at spatial infinities in the thermal state. We argue that correlation functions of light operators in such a state can be v...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: Springer Science and Business Media LLC 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa52119
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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∆ ∼ 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 rescaledeffective 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 ∆ < 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_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 ∆ =−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 λ_L = 4π/β, violating the universal chaos bound.
Issue: 10

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