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)} 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} . 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{4pi }{beta } , violating the universal chaos bound.
Highlights
We present a specific realization of this situation in the holographic Chern-Simons formulation of a conformal field theory (CFT) with W3(2) symmetry known as the Bershadsky-Polyakov algebra
It is well known that unitarity and causality in conformal field theories (CFTs) have been used to constrain the allowed spectra as well as to classify the allowed theories
It is such a ground state which is responsible for a positive single interval entanglement entropy in CFTs with c < 0 like the Lee-Yang non-unitary minimal model at c = −22/5 [13]. We demonstrate that such examples can arise holographically, i.e. vacua with ∆Φ < 0 and |∆Φ| ∼ O(c) are realised in semiclassical holographic setups at large-c. For this we examine the holographic realization of a CFT with a W3(2) symmetry
Summary
It is well known that unitarity and causality in conformal field theories (CFTs) have been used to constrain the allowed spectra as well as to classify the allowed theories. Wilson line correlator can be used to compute the change in EE following a local quench which can be viewed as an infalling conical deficit state Following this correlator by analytic continuation into the Regge limit [20] we obtain the OTO four point-function and show that the bound of [6] on the Lyapunov exponent is violated as would be expected in eq. We examine the representation theory of this algebra in the semiclassical limit and see how its nontrivial features are reproduced by the Chern-Simons framework This allows the identification of the ground state as Sections and deal with evaluation of holographic entanglement entropy using the Wilson line prescription.
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