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# Lightcone Modular Bootstrap and Pure Gravity

Benjamin, Nathan and Ooguri, Hirosi and Shao, Shu-Heng and Wang, Yifan (2019) Lightcone Modular Bootstrap and Pure Gravity. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20190709-155709037

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## Abstract

We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the lightcone limit. By recursively solving the modular crossing equations associated to different $PSL(2,\mathbb{Z})$ 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 $PSL(2,\mathbb{Z})$ 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 non-vacuum Virasoro primary whose twist is no bigger than $c-1\over16$. This suggests a new upper bound of $c-1\over 16$ 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 $\mathcal{N}=(1,1)$ supersymmetry, and find similar results.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1906.04184arXivDiscussion Paper
ORCID:
AuthorORCID
Ooguri, Hirosi0000-0001-6021-3778
Shao, Shu-Heng0000-0003-1294-2786
Wang, Yifan0000-0001-9965-9777
Additional Information: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 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 PHY-1606531 and by the Roger Dashen Membership. The work of Y.W. is supported in part by the US 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 PHY-1607611, where part of this work was done.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Simons Foundation488653
Department of Energy (DOE)DE-SC0011632
Japan Society for the Promotion of Science (JSPS)C-26400240
NSFPHY-1606531
NSFPHY-1607611
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2019-020
Record Number:CaltechAUTHORS:20190709-155709037
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190709-155709037
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97017
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:09 Jul 2019 23:37