Kaidi, Justin and Lin, Ying-Hsuan and Parra-Martinez, Julio (2021) Holomorphic modular bootstrap revisited. Journal of High Energy Physics, 2021 (12). Art. No. 151. ISSN 1029-8479. doi:10.1007/jhep12(2021)151. https://resolver.caltech.edu/CaltechAUTHORS:20220110-620552800
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Abstract
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, 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.
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| Additional Information: | © 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: August 18, 2021; Accepted: November 23, 2021; Published: December 21, 2021. We are grateful to Eric Perlmutter for collaboration until the late stages of this project. We thank Nathan Benjamin and Eric Perlmutter for comments on the first draft, and Yang-Hui He for sharing data on the character tables of finite subgroups of SL(3,C) and SL(4,C). We also thank Ana Martínez Pastor for various group-theoretic consultations. J.P.-M. also thanks her for being his mother. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. YL is supported by the Simons Bootstrap collaboration. | |||||||||
| Group: | Walter Burke Institute for Theoretical Physics | |||||||||
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| Subject Keywords: | Conformal Field Theory, Field Theories in Lower Dimensions | |||||||||
| Issue or Number: | 12 | |||||||||
| DOI: | 10.1007/jhep12(2021)151 | |||||||||
| Record Number: | CaltechAUTHORS:20220110-620552800 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20220110-620552800 | |||||||||
| Official Citation: | Kaidi, J., Lin, YH. & Parra-Martinez, J. Holomorphic modular bootstrap revisited. J. High Energ. Phys. 2021, 151 (2021). https://doi.org/10.1007/JHEP12(2021)151 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 112816 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 10 Jan 2022 23:35 | |||||||||
| Last Modified: | 10 Jan 2022 23:35 |
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