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Published September 15, 2019 | Submitted + Published
Journal Article Open

Light-cone modular bootstrap and pure gravity

Abstract

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.

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.

Attached Files

Published - PhysRevD.100.066029.pdf

Submitted - 1906.04184.pdf

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August 19, 2023
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