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Chaos bound in Bershadsky-Polyakov theory

David, Justin R and Hollowood, Timothy J and Khetrapal, Surbhi and Kumar, S. Prem (2019) Chaos bound in Bershadsky-Polyakov theory. In: JOURNAL OF HIGH ENERGY PHYSICS (10).

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Official URL: https://dx.doi.org/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 Phi with large dimension Delta(Phi) similar to 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-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) = -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.

Item Type: Journal Article
Additional Information: copyright to this article belongs to Springer Verlag
Keywords: AdS-CFT Correspondence; Conformal and W Symmetry; Conformal Field Theory; Higher Spin Gravity
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 15 Nov 2019 05:49
Last Modified: 15 Nov 2019 05:49
URI: http://eprints.iisc.ac.in/id/eprint/63898

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