Bootstrapping fermionic rational CFTs with three characters
Abstract Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γ θ , Γ0(2) and Γ0(2) of SL2(ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles we...
Main Authors: | , , , , |
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Format: | Article |
Language: | English |
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SpringerOpen
2022-01-01
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Series: | Journal of High Energy Physics |
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Online Access: | https://doi.org/10.1007/JHEP01(2022)089 |
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author | Jin-Beom Bae Zhihao Duan Kimyeong Lee Sungjay Lee Matthieu Sarkis |
author_facet | Jin-Beom Bae Zhihao Duan Kimyeong Lee Sungjay Lee Matthieu Sarkis |
author_sort | Jin-Beom Bae |
collection | DOAJ |
description | Abstract Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γ θ , Γ0(2) and Γ0(2) of SL2(ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound h R ≥ C 24 $$ \frac{C}{24} $$ , which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce K(τ), the character of the c = 12 fermionic CFT for Co0 sporadic group. |
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institution | Directory Open Access Journal |
issn | 1029-8479 |
language | English |
last_indexed | 2024-12-13T13:49:34Z |
publishDate | 2022-01-01 |
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series | Journal of High Energy Physics |
spelling | doaj.art-cfaafbb245464f10b4ce18d5b8cff9972022-12-21T23:43:16ZengSpringerOpenJournal of High Energy Physics1029-84792022-01-012022116010.1007/JHEP01(2022)089Bootstrapping fermionic rational CFTs with three charactersJin-Beom Bae0Zhihao Duan1Kimyeong Lee2Sungjay Lee3Matthieu Sarkis4Mathematical Institute, University of OxfordKorea Institute for Advanced StudyKorea Institute for Advanced StudyKorea Institute for Advanced StudyKorea Institute for Advanced StudyAbstract Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups Γ θ , Γ0(2) and Γ0(2) of SL2(ℤ) was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound h R ≥ C 24 $$ \frac{C}{24} $$ , which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce K(τ), the character of the c = 12 fermionic CFT for Co0 sporadic group.https://doi.org/10.1007/JHEP01(2022)089Conformal Field TheoryField Theories in Lower Dimensions |
spellingShingle | Jin-Beom Bae Zhihao Duan Kimyeong Lee Sungjay Lee Matthieu Sarkis Bootstrapping fermionic rational CFTs with three characters Journal of High Energy Physics Conformal Field Theory Field Theories in Lower Dimensions |
title | Bootstrapping fermionic rational CFTs with three characters |
title_full | Bootstrapping fermionic rational CFTs with three characters |
title_fullStr | Bootstrapping fermionic rational CFTs with three characters |
title_full_unstemmed | Bootstrapping fermionic rational CFTs with three characters |
title_short | Bootstrapping fermionic rational CFTs with three characters |
title_sort | bootstrapping fermionic rational cfts with three characters |
topic | Conformal Field Theory Field Theories in Lower Dimensions |
url | https://doi.org/10.1007/JHEP01(2022)089 |
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