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Title: Quantum Regge trajectories and the Virasoro analytic bootstrap

Abstract

Every conformal field theory (CFT) above two dimensions contains an infinite set of Regge trajectories of local operators which, at large spin, asymptote to “double-twist” composites with vanishing anomalous dimension. In two dimensions, due to the existence of local conformal symmetry, this and other central results of the conformal bootstrap do not apply. We incorporate exact stress tensor dynamics into the CFT2 analytic bootstrap, and extract several implications for AdS3 quantum gravity. Our main tool is the Virasoro fusion kernel, which we newly analyze and interpret in the bootstrap context. The contribution to double-twist data from the Virasoro vacuum module defines a “Virasoro Mean Field Theory” (VMFT); its spectrum includes a finite number of discrete Regge trajectories, whose dimensions obey a simple formula exact in the central charge c and external operator dimensions. We then show that VMFT provides a baseline for large spin universality in two dimensions: in every unitary compact CFT2 with c > 1 and a twist gap above the vacuum, the double-twist data approaches that of VMFT at large spin ℓ. Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in √ℓ for fixed c. We analyze our results in various largemore » c limits. Further applications include a derivation of the late-time behavior of Virasoro blocks at generic c; a refined understanding and new derivation of heavy-light blocks; and the determination of the cross-channel limit of generic Virasoro blocks. We deduce non-perturbative results about the bound state spectrum and dynamics of quantum gravity in AdS3.« less

Authors:
 [1];  [2];  [3];  [4]
+ Show Author Affiliations
  1. Harvard Univ., Cambridge, MA (United States)
  2. McGill Univ., Montreal, QC (Canada)
  3. McGill Univ., Montreal, QC (Canada); Univ. of California, Santa Barbara, CA (United States)
  4. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; Walter Burke Institute for Theoretical Physics; Natural Sciences and Engineering Research Council of Canada (NSERC); National Science Foundation (NSF)
OSTI Identifier:
1611635
Grant/Contract Number:  
SC0011632; 488657; 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: 2019; Journal Issue: 5; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Physics; AdS-CFT Correspondence; Conformal Field Theory; Gauge-gravity correspondence

Citation Formats

Collier, Scott, Gobeil, Yan, Maxfield, Henry, and Perlmutter, Eric. Quantum Regge trajectories and the Virasoro analytic bootstrap. United States: N. p., 2019. Web. doi:10.1007/jhep05(2019)212.
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Collier, Scott, Gobeil, Yan, Maxfield, Henry, & Perlmutter, Eric. Quantum Regge trajectories and the Virasoro analytic bootstrap. United States. https://doi.org/10.1007/jhep05(2019)212
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Collier, Scott, Gobeil, Yan, Maxfield, Henry, and Perlmutter, Eric. Fri . "Quantum Regge trajectories and the Virasoro analytic bootstrap". United States. https://doi.org/10.1007/jhep05(2019)212. https://www.osti.gov/servlets/purl/1611635.
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@article{osti_1611635,
title = {Quantum Regge trajectories and the Virasoro analytic bootstrap},
author = {Collier, Scott and Gobeil, Yan and Maxfield, Henry and Perlmutter, Eric},
abstractNote = {Every conformal field theory (CFT) above two dimensions contains an infinite set of Regge trajectories of local operators which, at large spin, asymptote to “double-twist” composites with vanishing anomalous dimension. In two dimensions, due to the existence of local conformal symmetry, this and other central results of the conformal bootstrap do not apply. We incorporate exact stress tensor dynamics into the CFT2 analytic bootstrap, and extract several implications for AdS3 quantum gravity. Our main tool is the Virasoro fusion kernel, which we newly analyze and interpret in the bootstrap context. The contribution to double-twist data from the Virasoro vacuum module defines a “Virasoro Mean Field Theory” (VMFT); its spectrum includes a finite number of discrete Regge trajectories, whose dimensions obey a simple formula exact in the central charge c and external operator dimensions. We then show that VMFT provides a baseline for large spin universality in two dimensions: in every unitary compact CFT2 with c > 1 and a twist gap above the vacuum, the double-twist data approaches that of VMFT at large spin ℓ. Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in √ℓ for fixed c. We analyze our results in various large c limits. Further applications include a derivation of the late-time behavior of Virasoro blocks at generic c; a refined understanding and new derivation of heavy-light blocks; and the determination of the cross-channel limit of generic Virasoro blocks. We deduce non-perturbative results about the bound state spectrum and dynamics of quantum gravity in AdS3.},
doi = {10.1007/jhep05(2019)212},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2019,
place = {United States},
year = {Fri May 31 00:00:00 EDT 2019},
month = {Fri May 31 00:00:00 EDT 2019}
}
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https://doi.org/10.1007/jhep05(2019)212
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text, January 2018

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