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Light-cone modular bootstrap and pure gravity

Benjamin, Nathan and Ooguri, Hirosi and Shao, Shu-Heng and Wang, Yifan (2019) Light-cone modular bootstrap and pure gravity. Physical Review D, 100 (6). Art. No. 066029. ISSN 2470-0010. doi:10.1103/PhysRevD.100.066029.

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We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the light-cone limit. By recursively solving the modular crossing equations associated with different PSL(2,Z) elements, we identify the universal contribution to the density of large spin states from the vacuum in the dual channel. Our result takes the form of a sum over PSL(2,Z) elements, whose leading term generalizes the usual Cardy formula to a wider regime. Rather curiously, the contribution to the density of states from the vacuum becomes negative in a specific limit, which can be canceled by that from a nonvacuum Virasoro primary whose twist is no bigger than c−1/16. This suggests a new upper bound of c−1/16 on the twist gap in any c>1 compact, unitary conformal field theory with a vacuum, which would in particular imply that pure AdS_3 gravity does not exist. We confirm this negative density of states in the pure gravity partition function by Maloney, Witten, and Keller. We generalize our discussion to theories with N=(1,1) supersymmetry and find similar results.

Item Type:Article
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URLURL TypeDescription Paper
Benjamin, Nathan0000-0003-3661-6563
Ooguri, Hirosi0000-0001-6021-3778
Shao, Shu-Heng0000-0003-1294-2786
Wang, Yifan0000-0001-9965-9777
Alternate Title:Lightcone Modular Bootstrap and Pure Gravity
Additional Information:© 2019 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. Received 7 July 2019; published 23 September 2019. We thank S. Collier, T. Hartman, S. Kachru, Z. Komargodski, Y.-H. Lin, R. Mahajan, A. Maloney, H. Maxfield, D. Mazac, B. Mukhametzhanov, E. Perlmutter, L. Rastelli, D. Simmons-Duffin, D. Stanford, H. Verlinde, and E. Witten for interesting discussions. We thank T. Hartman, C. Keller, A. Maloney, H. Maxfield, and X. Yin for comments on a draft. The work of N. B. is supported in part by the Simons Foundation Grant No. 488653. The work of H. O. is supported in part by U.S. Department of Energy Grant No. DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. The work of S. H. S. is supported by the National Science Foundation Grant No. PHY-1606531 and by the Roger Dashen Membership. The work of Y.W. is supported in part by the U.S. NSF under Grant No. PHY-1620059 and by the Simons Foundation Grant No. 488653. N. B. and H. O. thank the Aspen Center for Theoretical Physics, which is supported by the National Science Foundation Grant No. PHY-1607611, where part of this work was done.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation488653
Department of Energy (DOE)DE-SC0011632
Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
Japan Society for the Promotion of Science (JSPS)C-26400240
Japan Society for the Promotion of Science (JSPS)15H05895
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Issue or Number:6
Record Number:CaltechAUTHORS:20190709-155709037
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97017
Deposited By: Joy Painter
Deposited On:09 Jul 2019 23:37
Last Modified:16 Nov 2021 17:25

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