Holomorphic modular bootstrap revisited

Kaidi, Justin; Lin, Ying-Hsuan; Parra-Martinez, Julio

doi:10.1007/jhep12(2021)151

Title: Holomorphic modular bootstrap revisited

Journal Article · 20 December 2021 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep12(2021)151 · OSTI ID:1976597

Kaidi, Justin ^[1]; Lin, Ying-Hsuan ^[2]; Parra-Martinez, Julio ^[3]

Stony Brook University, NY (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
Harvard University, Cambridge, MA (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States)

In this work we revisit the “holomorphic modular bootstrap”, i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the representation theory of PSL(2, $$\mathbb{Z}_n$$), we describe a method to classify allowed central charges and weights (c, h_i) for theories with any number of characters d. This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to d = 5 whose modular differential equations are uniquely fixed in terms of (c, h_i). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed d ≤ 5.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: Simons Bootstrap Collaboration; USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011632

OSTI ID:: 1976597

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

References (41)

The Magma Algebra System I: The User Language Bosma, Wieb; Cannon, John; Playoust, Catherine Journal of Symbolic Computation, Vol. 24, Issue 3-4 https://doi.org/10.1006/jsco.1996.0125	journal	September 1997
Lectures on RCFT Moore, Gregory; Seiberg, Nathan Physics, Geometry and Topology, p. 263-361 https://doi.org/10.1007/978-1-4615-3802-8_8	book	January 1990
Rationality in conformal field theory Anderson, Greg; Moore, Greg Communications in Mathematical Physics, Vol. 117, Issue 3 https://doi.org/10.1007/BF01223375	journal	September 1988
Monodromy for the hypergeometric function n F n ?1 Beukers, F.; Heckman, G. Inventiones Mathematicae, Vol. 95, Issue 2 https://doi.org/10.1007/BF01393900	journal	June 1989
Modular invariance and uniqueness of conformal characters Eholzer, Wolfgang; Skoruppa, Nils-Peter Communications in Mathematical Physics, Vol. 174, Issue 1 https://doi.org/10.1007/BF02099466	journal	November 1995
On the classification of modular fusion algebras Eholzer, Wolfgang Communications in Mathematical Physics, Vol. 172, Issue 3 https://doi.org/10.1007/BF02101810	journal	September 1995
Die irreduziblen Darstellungen der Gruppen SL2(Zp), insbesondere SL2(Z2). I. Teil Nobs, Alexandre Commentarii Mathematici Helvetici, Vol. 51, Issue 1 https://doi.org/10.1007/BF02568170	journal	December 1976
Die irreduziblen Darstellungen der Gruppen SL2(Zp), insbesondere SL2(Z2). II. Teil Nobs, Alexandre; Wolfart, Jürgen Commentarii Mathematici Helvetici, Vol. 51, Issue 1 https://doi.org/10.1007/BF02568171	journal	December 1976
On 2d Conformal Field Theories with two characters Hampapura, Harsha R.; Mukhi, Sunil Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)005	journal	January 2016
Discreteness and integrality in Conformal Field Theory Kaidi, Justin; Perlmutter, Eric Journal of High Energy Physics, Vol. 2021, Issue 2 https://doi.org/10.1007/JHEP02(2021)064	journal	February 2021
Towards a classification of two-character rational conformal field theories Chandra, A. Ramesh; Mukhi, Sunil Journal of High Energy Physics, Vol. 2019, Issue 4 https://doi.org/10.1007/JHEP04(2019)153	journal	April 2019
Wronskian indices and rational conformal field theories Das, Arpit; Gowdigere, Chethan N.; Santara, Jagannath Journal of High Energy Physics, Vol. 2021, Issue 4 https://doi.org/10.1007/JHEP04(2021)294	journal	April 2021
Rational CFT with three characters: the quasi-character approach Mukhi, Sunil; Poddar, Rahul; Singh, Palash Journal of High Energy Physics, Vol. 2020, Issue 5 https://doi.org/10.1007/JHEP05(2020)003	journal	May 2020
Two-dimensional RCFT’s without Kac-Moody symmetry Hampapura, Harsha R.; Mukhi, Sunil Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)138	journal	July 2016
Vertex operator algebras, Higgs branches, and modular differential equations Beem, Christopher; Rastelli, Leonardo Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/JHEP08(2018)114	journal	August 2018
On Classification of Modular Tensor Categories Rowell, Eric; Stong, Richard; Wang, Zhenghan Communications in Mathematical Physics, Vol. 292, Issue 2 https://doi.org/10.1007/s00220-009-0908-z	journal	August 2009
McKay’s E 6 Observation on the Largest Fischer Group Höhn, Gerald; Lam, Ching Hung; Yamauchi, Hiroshi Communications in Mathematical Physics, Vol. 310, Issue 2 https://doi.org/10.1007/s00220-011-1413-8	journal	January 2012
Conformal Field Theories with Sporadic Group Symmetry Bae, Jin-Beom; Harvey, Jeffrey A.; Lee, Kimyeong Communications in Mathematical Physics, Vol. 388, Issue 1 https://doi.org/10.1007/s00220-021-04207-7	journal	October 2021
Hypergeometric series, modular linear differential equations and vector-valued modular forms Franc, Cameron; Mason, Geoffrey The Ramanujan Journal, Vol. 41, Issue 1-3 https://doi.org/10.1007/s11139-014-9644-x	journal	December 2014
On the classification of rational conformal field theories Mathur, Samir D.; Mukhi, Sunil; Sen, Ashoke Physics Letters B, Vol. 213, Issue 3 https://doi.org/10.1016/0370-2693(88)91765-0	journal	October 1988
Atkin-Lehner symmetry Moore, Gregory Nuclear Physics B, Vol. 293 https://doi.org/10.1016/0550-3213(87)90067-8	journal	January 1987
Conformal and current algebras on a general Riemann surface Eguchi, Tohru; Ooguri, Hirosi Nuclear Physics B, Vol. 282 https://doi.org/10.1016/0550-3213(87)90686-9	journal	January 1987
Fusion rules and modular transformations in 2D conformal field theory Verlinde, Erik Nuclear Physics B, Vol. 300 https://doi.org/10.1016/0550-3213(88)90603-7	journal	January 1988
Differential equations for rational conformal characters Naculich, Stephen G. Nuclear Physics B, Vol. 323, Issue 2 https://doi.org/10.1016/0550-3213(89)90150-8	journal	September 1989
Group theoretic classification of rational conformal field theories with algebraic characters Mathur, Samir D.; Sen, Ashoke Nuclear Physics B, Vol. 327, Issue 3 https://doi.org/10.1016/0550-3213(89)90312-X	journal	December 1989
Reconstruction of conformal field theories from modular geometry on the torus Mathur, Samir D.; Mukhi, Sunil; Sen, Ashoke Nuclear Physics B, Vol. 318, Issue 2 https://doi.org/10.1016/0550-3213(89)90615-9	journal	May 1989
Comments on the links between su(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards Bauer, M.; Coste, A.; Itzykson, C. Journal of Geometry and Physics, Vol. 22, Issue 2 https://doi.org/10.1016/S0393-0440(96)00027-7	journal	May 1997
Finite and Disconnected Subgroups of SU ₃ and their Application to the Elementary‐Particle Spectrum Fairbairn, W. M.; Fulton, T.; Klink, W. H. Journal of Mathematical Physics, Vol. 5, Issue 8 https://doi.org/10.1063/1.1704204	journal	August 1964
Classification of extremal vertex operator algebras with two simple modules Grady, J. Connor; Lam, Ching Hung; Tener, James E. Journal of Mathematical Physics, Vol. 61, Issue 5 https://doi.org/10.1063/1.5121446	journal	May 2020
Non-abelian finite gauge theories Hanany, Amihay; He, Yang-Hui Journal of High Energy Physics, Vol. 1999, Issue 02 https://doi.org/10.1088/1126-6708/1999/02/013	journal	February 1999
A monograph on the classification of the discrete subgroups of SU(4) Hanany, Amihay; He, Yang-Hui Journal of High Energy Physics, Vol. 2001, Issue 02 https://doi.org/10.1088/1126-6708/2001/02/027	journal	February 2001
Conformal characters and the modular representation Bantay, Peter; Gannon, Terry Journal of High Energy Physics, Vol. 2006, Issue 02 https://doi.org/10.1088/1126-6708/2006/02/005	journal	February 2006
Modular differential equations and null vectors Gaberdiel, Matthias R.; Keller, Christoph A. Journal of High Energy Physics, Vol. 2008, Issue 09 https://doi.org/10.1088/1126-6708/2008/09/079	journal	September 2008
Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories Harvey, Jeffrey A.; Hu, Yichen; Wu, Yuxiao Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 33 https://doi.org/10.1088/1751-8121/ab8e03	journal	August 2020
Gorenstein quotient singularities in dimension three Yau, Stephen S. -T.; Yu, Yung Memoirs of the American Mathematical Society, Vol. 105, Issue 505 https://doi.org/10.1090/memo/0505	journal	January 1993
On Classification of Modular Categories by Rank: Table A.1 Bruillard, Paul; Ng, Siu-Hung; Rowell, Eric C. International Mathematics Research Notices, Vol. 2016, Issue 24 https://doi.org/10.1093/imrn/rnw020	journal	April 2016
Conformal Invariance, Unitarity, and Critical Exponents in Two Dimensions Friedan, Daniel; Qiu, Zongan; Shenker, Stephen Physical Review Letters, Vol. 52, Issue 18 https://doi.org/10.1103/PhysRevLett.52.1575	journal	April 1984
Congruence property in conformal field theory Dong, Chongying; Lin, Xingjun; Ng, Siu-Hung Algebra & Number Theory, Vol. 9, Issue 9 https://doi.org/10.2140/ant.2015.9.2121	journal	November 2015
Classification of some vertex operator algebras of rank 3 Franc, Cameron; Mason, Geoffrey Algebra & Number Theory, Vol. 14, Issue 6 https://doi.org/10.2140/ant.2020.14.1613	journal	January 2020
Lessons from the Ramond sector Benjamin, Nathan; Lin, Ying-Hsuan SciPost Physics, Vol. 9, Issue 5 https://doi.org/10.21468/SciPostPhys.9.5.065	journal	January 2020
Finite Unitary Reflection Groups Shephard, G. C.; Todd, J. A. Canadian Journal of Mathematics, Vol. 6 https://doi.org/10.4153/CJM-1954-028-3	journal	January 1954

Similar Records

Improving modular bootstrap bounds with integrality

Journal Article · 2024 · Journal of High Energy Physics (Online) · OSTI ID:2576076

Fitzpatrick, A. Liam; Li, Wei

Lessons from the Ramond sector

Journal Article · 2020 · SciPost Physics · OSTI ID:1706204

Benjamin, Nathan; Lin, Ying-Hsuan

Modular bootstrap revisited

Journal Article · 2018 · Journal of High Energy Physics (Online) · OSTI ID:1507580

Collier, Scott; Lin, Ying -Hsuan; Yin, Xi

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
conformal field theory
field theories in lower dimensions

Title: Holomorphic modular bootstrap revisited

Citation Formats

References (41)

Similar Records

Related Subjects