Conformal field theory and the web of quantum chaos diagnostics

Jonah Kudler-Flam (Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL, 60637, USA) ; Laimei Nie (Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL, 60637, USA) ; Shinsei Ryu (Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL, 60637, USA; James Franck Institute, University of Chicago, Chicago, Illinois, 60637, USA)

We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that all three quantities may be obtained by different analytic continuations of the torus partition function, we address the connections and distinctions between the information that each quantity provides us. In this process, we study the emergence of irrationality from “large-N” limits of rational conformal field theories (RCFTs) as well as the explicit breakdown of rationality for theories with central charges greater than the number of their conserved currents. Our analysis begins to elucidate the intermediate dynamical behavior of theories that bridge the gap between integrable RCFTs and maximally chaotic holographic CFTs.

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Published on:
28 January 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 1
Pages 1-33
DOI:
https://doi.org/10.1007/JHEP01(2020)175
arXiv:
1910.14575
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: