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Notes on Scrambling in Conformal Field Theory · Around

2018

Notes on Scrambling in Conformal Field Theory

Liu, Chang, Lowe, David A.

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The onset of quantum chaos in quantum field theory may be studied using out-of-time-order correlators at finite temperature.

Recent work argued that a timescale logarithmic in the central charge emerged in the context of two-dimensional conformal field theories, provided the intermediate channel was dominated by the Virasoro identity block.
This suggests a wide class of conformal field theories exhibit a version of fast scrambling.
In the present work we study this idea in more detail.

Built on

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A. B. Zamolodchikov, “Conformal symmetry in two-dimensional space: Recursion representation of conformal block,” Theor. Math. Phys
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D. A. Lowe, “The Planckian conspiracy: String theory and the black hole information paradox,” Nucl. Phys
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Earlier work this paper cites.

Similar

D. A. Lowe, J. Polchinski, L. Susskind, L. Thorlacius, and J. Uglum, “Black hole complementarity versus locality,” Phys. Rev
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A. L. Fitzpatrick, J. Kaplan, and M. T. Walters, “Universality of Long-Distance AdS Physics from the CFT Bootstrap,” JHEP
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D. A. Roberts and D. Stanford, “Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory,” Phys. Rev. Lett
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2015
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A. L. Fitzpatrick, J. Kaplan, and M. T. Walters, “Virasoro Conformal Blocks and Thermality from Classical Background Fields,” JHEP
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“Wolfram Research, Gauss Hypergeometric Function, Series Expansion, Formula 07.23.06.0013.01. http://functions.wolfram.com/07.23.06.0013.01
Cited in the paper.
We clarify that in most mathematical literature, the complete elliptic integral K K is defined with the modulus k k as the argument. Our z z is related to k k through z = k 2 z=k^{2} . It is also common for many mathematicians to use the symbol m m for our z z
Cited in the paper.
R. Fan, “Out-of-Time-Order Correlation Functions for Unitary Minimal Models,” arXiv:1809.07228 [hep-th]
Original
Cited in the paper.

Then

A. L. Fitzpatrick, J. Kaplan, D. Li, and J. Wang, “On information loss in AdS 3
Original
2016
Later among the works it cites.
A. L. Fitzpatrick and J. Kaplan, “On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles,” JHEP
Original
2017
Later among the works it cites.
C. Bogner, A. Schweitzer, and S. Weinzierl, “Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral,” Nucl. Phys
Original
2017
Later among the works it cites.
Y. Sekino and L. Susskind, “Fast Scramblers,” JHEP
Original
2096
Closest in time.

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