DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 1 6 . This suggests a new upper bound of c - 1 1 6 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

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3];  [4]
  1. Princeton Univ., NJ (United States)
  2. California Institute of Technology (CalTech), Pasadena, CA (United States); Univ. of Tokyo (Japan)
  3. Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  4. 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; PHY-1606531; PHY-1620059; PHY-1607611
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 100; Journal Issue: 6; Journal ID: ISSN 2470-0010
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, Shu-Heng, and Wang, Yifan. Light-cone modular bootstrap and pure gravity. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.066029.
Benjamin, Nathan, Ooguri, Hirosi, Shao, Shu-Heng, & Wang, Yifan. Light-cone modular bootstrap and pure gravity. United States. https://doi.org/10.1103/PhysRevD.100.066029
Benjamin, Nathan, Ooguri, Hirosi, Shao, Shu-Heng, and Wang, Yifan. Mon . "Light-cone modular bootstrap and pure gravity". United States. https://doi.org/10.1103/PhysRevD.100.066029.
@article{osti_1564551,
title = {Light-cone modular bootstrap and pure gravity},
author = {Benjamin, Nathan and Ooguri, Hirosi and Shao, Shu-Heng and Wang, Yifan},
abstractNote = {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-116. This suggests a new upper bound of c-116 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.100.066029

Citation Metrics:
Cited by: 52 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Quantum gravity partition functions in three dimensions
journal, February 2010

  • Maloney, Alexander; Witten, Edward
  • Journal of High Energy Physics, Vol. 2010, Issue 2
  • DOI: 10.1007/JHEP02(2010)029

Charged structure constants from modularity
journal, November 2017

  • Das, Diptarka; Datta, Shouvik; Pal, Sridip
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)183

Operator content of two-dimensional conformally invariant theories
journal, January 1986


The large $N$ limit of superconformal field theories and supergravity
journal, January 1998


Bootstrapping the spectral function: on the uniqueness of Liouville and the universality of BTZ
journal, September 2018

  • Collier, Scott; Kravchuk, Petr; Lin, Ying-Hsuan
  • Journal of High Energy Physics, Vol. 2018, Issue 9
  • DOI: 10.1007/JHEP09(2018)150

Modular bootstrap revisited
journal, September 2018

  • Collier, Scott; Lin, Ying-Hsuan; Yin, Xi
  • Journal of High Energy Physics, Vol. 2018, Issue 9
  • DOI: 10.1007/JHEP09(2018)061

Charged structure constants from modularity
text, January 2017


Black hole entropy from near-horizon microstates
journal, February 1998


A conformal block Farey tail
journal, June 2017

  • Maloney, Alexander; Maxfield, Henry; Ng, Gim Seng
  • Journal of High Energy Physics, Vol. 2017, Issue 6
  • DOI: 10.1007/JHEP06(2017)117

Notes on the Verlinde formula in nonrational conformal field theories
journal, November 2006


The analytic bootstrap and AdS superhorizon locality
journal, December 2013

  • Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)004

Entanglement entropy, OTOC and bootstrap in 2D CFTs from Regge and light cone limits of multi-point conformal block
journal, August 2019


Closure of the operator product expansion in the non-unitary bootstrap
journal, November 2016

  • Esterlis, Ilya; Fitzpatrick, A. Liam; Ramirez, David M.
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)030

Poincaré series, 3D gravity and CFT spectroscopy
journal, February 2015

  • Keller, Christoph A.; Maloney, Alexander
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)080

Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity
journal, January 2019


Non-supersymmetric AdS and the swampland
journal, January 2017


AdS 3 black holes and a stringy exclusion principle
journal, December 1998


A universal inequality for CFT and quantum gravity
journal, August 2011


The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

  • Maldacena, Juan
  • International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133
  • DOI: 10.1023/A:1026654312961

Constraints on higher spin CFT2
journal, May 2018

  • Afkhami-Jeddi, Nima; Colville, Kale; Hartman, Thomas
  • Journal of High Energy Physics, Vol. 2018, Issue 5
  • DOI: 10.1007/JHEP05(2018)092

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap
journal, April 2017


Quantum Regge trajectories and the Virasoro analytic bootstrap
journal, May 2019

  • Collier, Scott; Gobeil, Yan; Maxfield, Henry
  • Journal of High Energy Physics, Vol. 2019, Issue 5
  • DOI: 10.1007/JHEP05(2019)212

Convexity and liberation at large spin
journal, November 2013

  • Komargodski, Zohar; Zhiboedov, Alexander
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)140

Minimal lectures on two-dimensional conformal field theory
journal, June 2018


The large N limit of superconformal field theories and supergravity
conference, January 1999

  • Maldacena, Juan
  • The second meeting on trends in theoretical physics, AIP Conference Proceedings
  • DOI: 10.1063/1.59653

Poincare Series, 3D Gravity and CFT Spectroscopy
text, January 2014


A conformal block Farey tail
text, January 2016


Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ
text, January 2017


Constraints on Higher Spin CFT$_2$
text, January 2017


Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
text, January 2018


Black Hole Entropy from Near-Horizon Microstates
text, January 1997


AdS3 Black Holes and a Stringy Exclusion Principle
text, January 1998