Two-dimensional conformal field theory and the butterfly effect

Abstract

We study chaotic dynamics in two-dimensional conformal field theory through out-of-time order thermal correlators of the form $⟨W(t)VW(t)V⟩$. We reproduce bulk calculations similar to those of [1], by studying the large $c$ Virasoro identity block. The contribution of this block to the above correlation function begins to decrease exponentially after a delay of $\sim t_{\ast }-\frac{\beta }{2\pi }\log {\beta }^2{E}_w{E}_v$, where $t_{\ast }$ is the scrambling time $\frac{\beta }{2\pi }\log c$, and $E_w,E_v$ are the energy scales of the $W,V$ operators.

v1: 14 pages plus appendices, 2 figures. v2: references updated and minor changes to the text. v3: minor error corrected in Appendix B, but the conclusion is unchanged

References in corpus (12)

• Black holes as mirrors: quantum information in random subsystems
• Complexity and Shock Wave Geometries
• Localized shocks
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Entanglement Entropy at Large Central Charge
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• Switchbacks and the Bridge to Nowhere
• Conformal Bootstrap, Universality and Gravitational Scattering
• Disrupting Entanglement of Black Holes
• Computational Complexity and Black Hole Horizons

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