Benjamin, Nathan and Ooguri, Hirosi and Shao, Shu-Heng and Wang, Yifan
(2019)
*Lightcone Modular Bootstrap and Pure Gravity.*
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(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.

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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 | ||||||||||||

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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 | ||||||||||||

Last Modified: | 09 Jul 2019 23:37 |

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