Lightcone modular bootstrap and pure gravity
Abstract
We explore the large spin spectrum in twodimensional conformal field theories with a finite twist gap, using the modular bootstrap in the lightcone limit. By recursively solving the modular crossing equations associated with 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 nonvacuum Virasoro primary whose twist is no bigger than $\frac{c1}{16}$. This suggests a new upper bound of $\frac{c1}{16}$ on the twist gap in any $c>1$ compact, unitary conformal field theory with a vacuum, which would in particular imply that pure ${\mathrm{AdS}}_{3}$ 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
 Authors:

 Princeton Univ., NJ (United States)
 California Institute of Technology (CalTech), Pasadena, CA (United States); Univ. of Tokyo (Japan)
 Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
 Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics
 Publication Date:
 Research Org.:
 California Institute of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; National Science Foundation (NSF)
 OSTI Identifier:
 1564551
 Alternate Identifier(s):
 OSTI ID: 1600526
 Grant/Contract Number:
 SC0011632; PHY1606531; PHY1620059; PHY1607611
 Resource Type:
 Published Article
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 100; Journal Issue: 6; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Benjamin, Nathan, Ooguri, Hirosi, Shao, ShuHeng, and Wang, Yifan. Lightcone modular bootstrap and pure gravity. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.066029.
Benjamin, Nathan, Ooguri, Hirosi, Shao, ShuHeng, & Wang, Yifan. Lightcone modular bootstrap and pure gravity. United States. https://doi.org/10.1103/PhysRevD.100.066029
Benjamin, Nathan, Ooguri, Hirosi, Shao, ShuHeng, and Wang, Yifan. Mon .
"Lightcone modular bootstrap and pure gravity". United States. https://doi.org/10.1103/PhysRevD.100.066029.
@article{osti_1564551,
title = {Lightcone modular bootstrap and pure gravity},
author = {Benjamin, Nathan and Ooguri, Hirosi and Shao, ShuHeng and Wang, Yifan},
abstractNote = {We explore the large spin spectrum in twodimensional conformal field theories with a finite twist gap, using the modular bootstrap in the lightcone 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 c116. This suggests a new upper bound of c116 on the twist gap in any c>1 compact, unitary conformal field theory with a vacuum, which would in particular imply that pure AdS3 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},
doi = {10.1103/PhysRevD.100.066029},
journal = {Physical Review D},
number = 6,
volume = 100,
place = {United States},
year = {2019},
month = {9}
}
https://doi.org/10.1103/PhysRevD.100.066029
Web of Science
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