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Quantum Regge trajectories and the Virasoro analytic bootstrap

Collier, Scott and Gobeil, Yan and Maxfield, Henry and Perlmutter, Eric (2019) Quantum Regge trajectories and the Virasoro analytic bootstrap. Journal of High Energy Physics, 2019 (5). Art. No. 212. ISSN 1029-8479. doi:10.1007/jhep05(2019)212.

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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 CFT_2 analytic bootstrap, and extract several implications for AdS_3 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 CFT_2 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 AdS_3.

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Additional Information:© 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: January 3, 2019; Revised: April 18, 2019; Accepted: May 20, 2019; Published: May 31, 2019. We thank Alex Belin, Minjae Cho, Shouvik Datta, Monica Guica, Per Kraus, Daliang Li, Junyu Liu, Don Marolf, David Meltzer, David Poland, David Simmons-Duffin, Douglas Stanford and Xi Yin for helpful discussions. We also thank Minjae Cho, Daliang Li, Alex Maloney and Xi Yin for comments on a draft. EP is supported by Simons Foundation grant 488657, and by the Walter Burke Institute for Theoretical Physics. SC and YG are supported in part by the Natural Sciences and Engineering Research Council of Canada via PGS D fellowships. YG is also supported by a Walter C. Sumner Memorial Fellowship. HM is funded by a Len DeBenedictis postdoctoral fellowship, and receives additional support from the University of California. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. We thank the Simons Nonperturbative Bootstrap 2018 conference, and the KITP workshop "Chaos and Order: From Strongly Correlated Systems to Black Holes," for stimulating environments during the course of this project. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488657
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Walter C. Sumner Memorial FellowshipUNSPECIFIED
Len DeBenedictis Postdoctoral FellowshipUNSPECIFIED
University of CaliforniaUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Subject Keywords:AdS-CFT Correspondence; Conformal Field Theory; Gauge-gravity correspondence
Issue or Number:5
Record Number:CaltechAUTHORS:20190612-084813113
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Official Citation:Collier, S., Gobeil, Y., Maxfield, H. et al. J. High Energ. Phys. (2019) 2019: 212.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96312
Deposited By: Tony Diaz
Deposited On:12 Jun 2019 16:42
Last Modified:16 Nov 2021 17:19

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