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Chaos bound in Bershadsky-Polyakov theory

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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 W3(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 ΔΦ=−c8. 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 λL=4πβ , violating the universal chaos bound.

Tijdschrift: Journal of High Energy Physics
ISSN: 1126-6708
Issue: 10
Volume: 2019
Jaar van publicatie:2019
Trefwoorden:hep-th
CSS-citation score:1
Toegankelijkheid:Open