Chaos bound in Bershadsky-Polyakov theory

  • Justin R. David
  • Timothy J. Hollowood
  • Surbhi Khetrapal
  • S. Prem KumarEmail author
Open Access
Regular Article - Theoretical Physics


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.


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


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Justin R. David
    • 1
  • Timothy J. Hollowood
    • 2
  • Surbhi Khetrapal
    • 3
  • S. Prem Kumar
    • 2
    Email author
  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceBangaloreIndia
  2. 2.Department of PhysicsSwansea UniversitySwanseaU.K.
  3. 3.Theoretische NatuurkundeVrije Universiteit Brussel (VUB) and The International Solvay InstitutesBrusselsBelgium

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