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:
-
- 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.
Collier, Scott, Lin, Ying -Hsuan, & Yin, Xi. Modular bootstrap revisited. United States. doi:10.1007/jhep09(2018)061.
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.
@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}
}
Web of Science
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
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
Constraints on 2d CFT partition functions
journal, October 2013
- Friedan, Daniel; Keller, Christoph A.
- Journal of High Energy Physics, Vol. 2013, Issue 10
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
Coupled Potts models: Self-duality and fixed point structure
journal, May 1999
- Dotsenko, Vladimir; Jacobsen, Jesper Lykke; Lewis, Marc-André
- Nuclear Physics B, Vol. 546, Issue 3
Radial coordinates for conformal blocks
journal, May 2013
- Hogervorst, Matthijs; Rychkov, Slava
- Physical Review D, Vol. 87, Issue 10
A universal inequality for CFT and quantum gravity
journal, August 2011
- Hellerman, Simeon
- Journal of High Energy Physics, Vol. 2011, Issue 8
Constraining conformal field theories with a higher spin symmetry
journal, May 2013
- Maldacena, Juan; Zhiboedov, Alexander
- Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 21
Bootstrapping 2D CFTs in the semiclassical limit
journal, August 2016
- Chang, Chi-Ming; Lin, Ying-Hsuan
- Journal of High Energy Physics, Vol. 2016, Issue 8
Irrational conformal field theory
journal, February 1996
- Halpern, M. B.; Kiritsis, E.; Obers, N. A.
- Physics Reports, Vol. 265, Issue 1-2
Bounding the space of holographic CFTs with chaos
journal, October 2016
- Perlmutter, Eric
- Journal of High Energy Physics, Vol. 2016, Issue 10
The effective bootstrap
journal, September 2016
- Echeverri, Alejandro Castedo; von Harling, Benedict; Serone, Marco
- Journal of High Energy Physics, Vol. 2016, Issue 9
Classical and quantum conformal field theory
journal, June 1989
- Moore, Gregory; Seiberg, Nathan
- Communications in Mathematical Physics, Vol. 123, Issue 2
Bootstrapping Conformal Field Theories with the Extremal Functional Method
journal, December 2013
- El-Showk, Sheer; Paulos, Miguel F.
- Physical Review Letters, Vol. 111, Issue 24
Large N field theories, string theory and gravity
journal, January 2000
- Aharony, Ofer; Gubser, Steven S.; Maldacena, Juan
- Physics Reports, Vol. 323, Issue 3-4
Modular Constraints on Calabi-Yau Compactifications
journal, September 2013
- Keller, Christoph A.; Ooguri, Hirosi
- Communications in Mathematical Physics, Vol. 324, Issue 1
On the unitary representations of N=2 and N=4 superconformal algebras
journal, August 1988
- Eguchi, Tohru; Taormina, Anne
- Physics Letters B, Vol. 210, Issue 1-2
A semidefinite program solver for the conformal bootstrap
journal, June 2015
- Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2015, Issue 6
Non-abelian bosonization in two dimensions
journal, December 1984
- Witten, Edward
- Communications in Mathematical Physics, Vol. 92, Issue 4
Rigorous limits on the interaction strength in quantum field theory
journal, April 2010
- Caracciolo, Francesco; Rychkov, Slava
- Physical Review D, Vol. 81, Issue 8
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
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
Fusion rules and modular transformations in 2D conformal field theory
journal, January 1988
- Verlinde, Erik
- Nuclear Physics B, Vol. 300
Perfect metal phases of one-dimensional and anisotropic higher-dimensional systems
journal, December 2014
- Plamadeala, Eugeniu; Mulligan, Michael; Nayak, Chetan
- Physical Review B, Vol. 90, Issue 24
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
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
Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity
journal, January 2019
- Kusuki, Yuya
- Journal of High Energy Physics, Vol. 2019, Issue 1
Bound on asymptotics of magnitude of three point coefficients in 2D CFT
journal, January 2020
- Pal, Sridip
- Journal of High Energy Physics, Vol. 2020, Issue 1
Genus two modular bootstrap
journal, April 2019
- Cho, Minjae; Collier, Scott; Yin, Xi
- Journal of High Energy Physics, Vol. 2019, Issue 4
The most irrational rational theories
journal, April 2019
- Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam
- Journal of High Energy Physics, Vol. 2019, Issue 4
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
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
Einstein gravity from ANEC correlators
journal, August 2019
- Belin, Alexandre; Hofman, Diego M.; Mathys, Grégoire
- Journal of High Energy Physics, Vol. 2019, Issue 8
Entanglement entropy, OTOC and bootstrap in 2D CFTs from Regge and light cone limits of multi-point conformal block
journal, August 2019
- Kusuki, Yuya; Miyaji, Masamichi
- Journal of High Energy Physics, Vol. 2019, Issue 8
Growing extra dimensions in AdS/CFT
journal, August 2019
- Alday, Luis F.; Perlmutter, Eric
- Journal of High Energy Physics, Vol. 2019, Issue 8
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
Analytic Euclidean bootstrap
journal, October 2019
- Mukhametzhanov, Baur; Zhiboedov, Alexander
- Journal of High Energy Physics, Vol. 2019, Issue 10
Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
journal, December 2019
- Maxfield, Henry
- Journal of High Energy Physics, Vol. 2019, Issue 12
Sphere packing and quantum gravity
journal, December 2019
- Hartman, Thomas; Mazáč, Dalimil; Rastelli, Leonardo
- Journal of High Energy Physics, Vol. 2019, Issue 12
Anomalies and bounds on charged operators
journal, July 2019
- Lin, Ying-Hsuan; Shao, Shu-Heng
- Physical Review D, Vol. 100, Issue 2
Light-cone modular bootstrap and pure gravity
journal, September 2019
- Benjamin, Nathan; Ooguri, Hirosi; Shao, Shu-Heng
- Physical Review D, Vol. 100, Issue 6
Chiral modular bootstrap
journal, October 2019
- Ashrafi, M.
- International Journal of Modern Physics A, Vol. 34, Issue 28