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Chaos bound in Bershadsky-Polyakov theory

  • Regular Article - Theoretical Physics
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  • Published: 07 October 2019
  • volume 2019, Article number: 77 (2019)
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Chaos bound in Bershadsky-Polyakov theory
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  • Justin R. David1,
  • Timothy J. Hollowood2,
  • Surbhi Khetrapal3 &
  • …
  • S. Prem Kumar2 
  • 253 Accesses

  • 7 Citations

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A preprint version of the article is available at arXiv.

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 \( {\uplambda}_L=\frac{4\pi }{\beta } \), violating the universal chaos bound.

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Authors and Affiliations

  1. Centre for High Energy Physics, Indian Institute of Science, C.V. Raman Avenue, Bangalore, 560012, India

    Justin R. David

  2. Department of Physics, Swansea University, Singleton Park, Swansea, SA2 8PP, U.K.

    Timothy J. Hollowood & S. Prem Kumar

  3. Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) and The International Solvay Institutes, Pleinlaan 2, B-1050, Brussels, Belgium

    Surbhi Khetrapal

Authors
  1. Justin R. David
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Corresponding author

Correspondence to S. Prem Kumar.

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ArXiv ePrint: 1906.00667

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David, J.R., Hollowood, T.J., Khetrapal, S. et al. Chaos bound in Bershadsky-Polyakov theory. J. High Energ. Phys. 2019, 77 (2019). https://doi.org/10.1007/JHEP10(2019)077

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  • Received: 06 July 2019

  • Accepted: 10 September 2019

  • Published: 07 October 2019

  • DOI: https://doi.org/10.1007/JHEP10(2019)077

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Keywords

  • AdS-CFT Correspondence
  • Conformal and W Symmetry
  • Conformal Field Theory
  • Higher Spin Gravity

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