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Title: On the Virasoro six-point identity block and chaos

Abstract

We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge $$c$$ and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block - corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor $$SL(2,\mathbb{R})$$ (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large $$c$$ as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks' relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Univ. of Amsterdam (Netherlands)
  2. Institute for Advanced Study, Princeton, NJ (United States)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1648324
Grant/Contract Number:  
SC0009988; PHY-1748958
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; AdS-CFT Correspondence; Effective Field Theories; Stochastic Processes

Citation Formats

Anous, Tarek, and Haehl, Felix M. On the Virasoro six-point identity block and chaos. United States: N. p., 2020. Web. doi:10.1007/jhep08(2020)002.
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Anous, Tarek, & Haehl, Felix M. On the Virasoro six-point identity block and chaos. United States. https://doi.org/10.1007/jhep08(2020)002
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Anous, Tarek, and Haehl, Felix M. Tue . "On the Virasoro six-point identity block and chaos". United States. https://doi.org/10.1007/jhep08(2020)002. https://www.osti.gov/servlets/purl/1648324.
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@article{osti_1648324,
title = {On the Virasoro six-point identity block and chaos},
author = {Anous, Tarek and Haehl, Felix M.},
abstractNote = {We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge $c$ and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block - corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor $SL(2,\mathbb{R})$ (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large $c$ as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks' relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.},
doi = {10.1007/jhep08(2020)002},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2020,
place = {United States},
year = {Tue Aug 04 00:00:00 EDT 2020},
month = {Tue Aug 04 00:00:00 EDT 2020}
}
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https://doi.org/10.1007/jhep08(2020)002
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    Works referencing / citing this record:

    Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges
    journal, May 2021

    Reparametrization mode Ward Identities and chaos in higher-pt. correlators in CFT$_2$
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