skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Modular bootstrap revisited

Abstract

We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.

Authors:
ORCiD logo [1];  [1];  [1]
+ Show Author Affiliations
  1. Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.
Publication Date:
Research Org.:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1507580
Grant/Contract Number:  
FG02-91ER40654
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Black Holes; Conformal and W Symmetry; Conformal Field Theory

Citation Formats

Collier, Scott, Lin, Ying -Hsuan, and Yin, Xi. Modular bootstrap revisited. United States: N. p., 2018. Web. doi:10.1007/jhep09(2018)061.
Copy to clipboard
Collier, Scott, Lin, Ying -Hsuan, & Yin, Xi. Modular bootstrap revisited. United States. doi:10.1007/jhep09(2018)061.
Copy to clipboard
Collier, Scott, Lin, Ying -Hsuan, and Yin, Xi. Wed . "Modular bootstrap revisited". United States. doi:10.1007/jhep09(2018)061. https://www.osti.gov/servlets/purl/1507580.
Copy to clipboard
@article{osti_1507580,
title = {Modular bootstrap revisited},
author = {Collier, Scott and Lin, Ying -Hsuan and Yin, Xi},
abstractNote = {We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.},
doi = {10.1007/jhep09(2018)061},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2018,
place = {United States},
year = {2018},
month = {9}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI:  10.1007/jhep09(2018)061
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 22 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Virasoro conformal blocks and thermality from classical background fields
journal, November 2015

  • Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)200

Universal spectrum of 2d conformal field theory in the large c limit
journal, September 2014

  • Hartman, Thomas; Keller, Christoph A.; Stoica, Bogdan
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)118

Constraints on 2d CFT partition functions
journal, October 2013

  • Friedan, Daniel; Keller, Christoph A.
  • Journal of High Energy Physics, Vol. 2013, Issue 10
  • DOI: 10.1007/JHEP10(2013)180

Universality of long-distance AdS physics from the CFT bootstrap
journal, August 2014

  • Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)145

Coupled Potts models: Self-duality and fixed point structure
journal, May 1999

Radial coordinates for conformal blocks
journal, May 2013

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

Constraining conformal field theories with a higher spin symmetry
journal, May 2013

Bootstrapping 2D CFTs in the semiclassical limit
journal, August 2016

Irrational conformal field theory
journal, February 1996

Bounding the space of holographic CFTs with chaos
journal, October 2016

The effective bootstrap
journal, September 2016

  • Echeverri, Alejandro Castedo; von Harling, Benedict; Serone, Marco
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)097

Classical and quantum conformal field theory
journal, June 1989

  • Moore, Gregory; Seiberg, Nathan
  • Communications in Mathematical Physics, Vol. 123, Issue 2
  • DOI: 10.1007/BF01238857

Bootstrapping Conformal Field Theories with the Extremal Functional Method
journal, December 2013

Large N field theories, string theory and gravity
journal, January 2000

Modular Constraints on Calabi-Yau Compactifications
journal, September 2013

  • Keller, Christoph A.; Ooguri, Hirosi
  • Communications in Mathematical Physics, Vol. 324, Issue 1
  • DOI: 10.1007/s00220-013-1797-8

On the unitary representations of N=2 and N=4 superconformal algebras
journal, August 1988

A semidefinite program solver for the conformal bootstrap
journal, June 2015

Non-abelian bosonization in two dimensions
journal, December 1984

  • Witten, Edward
  • Communications in Mathematical Physics, Vol. 92, Issue 4
  • DOI: 10.1007/BF01215276

Rigorous limits on the interaction strength in quantum field theory
journal, April 2010

Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents
journal, June 2014

  • El-Showk, Sheer; Paulos, Miguel F.; Poland, David
  • Journal of Statistical Physics, Vol. 157, Issue 4-5
  • DOI: 10.1007/s10955-014-1042-7

Bounds for state degeneracies in 2D conformal field theory
journal, August 2011

  • Hellerman, Simeon; Schmidt-Colinet, Cornelius
  • Journal of High Energy Physics, Vol. 2011, Issue 8
  • DOI: 10.1007/JHEP08(2011)127

Fusion rules and modular transformations in 2D conformal field theory
journal, January 1988

Perfect metal phases of one-dimensional and anisotropic higher-dimensional systems
journal, December 2014

Curiosities at c = 1
journal, February 1988

    [ × clear filter / sort ]

    Works referencing / citing this record:

    The analytic functional bootstrap. Part II. Natural bases for the crossing equation
    journal, February 2019

    • Mazáč, Dalimil; Paulos, Miguel F.
    • Journal of High Energy Physics, Vol. 2019, Issue 2
    • DOI: 10.1007/jhep02(2019)163

    The analytic functional bootstrap. Part II. Natural bases for the crossing equation
    journal, February 2019

    • Mazáč, Dalimil; Paulos, Miguel F.
    • Journal of High Energy Physics, Vol. 2019, Issue 2
    • DOI: 10.1007/jhep02(2019)163

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

    Bound on asymptotics of magnitude of three point coefficients in 2D CFT
    journal, January 2020

    Genus two modular bootstrap
    journal, April 2019

    • Cho, Minjae; Collier, Scott; Yin, Xi
    • Journal of High Energy Physics, Vol. 2019, Issue 4
    • DOI: 10.1007/jhep04(2019)022

    The most irrational rational theories
    journal, April 2019

    • Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam
    • Journal of High Energy Physics, Vol. 2019, Issue 4
    • DOI: 10.1007/jhep04(2019)025

    Fast conformal bootstrap and constraints on 3d gravity
    journal, May 2019

    • Afkhami-Jeddi, Nima; Hartman, Thomas; Tajdini, Amirhossein
    • Journal of High Energy Physics, Vol. 2019, Issue 5
    • DOI: 10.1007/jhep05(2019)087

    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

    Einstein gravity from ANEC correlators
    journal, August 2019

    • Belin, Alexandre; Hofman, Diego M.; Mathys, Grégoire
    • Journal of High Energy Physics, Vol. 2019, Issue 8
    • DOI: 10.1007/jhep08(2019)032

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

    Growing extra dimensions in AdS/CFT
    journal, August 2019

    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

    Analytic Euclidean bootstrap
    journal, October 2019

    • Mukhametzhanov, Baur; Zhiboedov, Alexander
    • Journal of High Energy Physics, Vol. 2019, Issue 10
    • DOI: 10.1007/jhep10(2019)270

    Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
    journal, December 2019

    Sphere packing and quantum gravity
    journal, December 2019

    • Hartman, Thomas; Mazáč, Dalimil; Rastelli, Leonardo
    • Journal of High Energy Physics, Vol. 2019, Issue 12
    • DOI: 10.1007/jhep12(2019)048

    Anomalies and bounds on charged operators
    journal, July 2019

    Light-cone modular bootstrap and pure gravity
    journal, September 2019

    Chiral modular bootstrap
    journal, October 2019

      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: