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...

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Main Authors: Jin-Beom Bae, Zhihao Duan, Kimyeong Lee, Sungjay Lee, Matthieu Sarkis
Format: Article
Language:English
Published: SpringerOpen 2022-01-01
Series:Journal of High Energy Physics
Subjects:
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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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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AT zhihaoduan bootstrappingfermionicrationalcftswiththreecharacters
AT kimyeonglee bootstrappingfermionicrationalcftswiththreecharacters
AT sungjaylee bootstrappingfermionicrationalcftswiththreecharacters
AT matthieusarkis bootstrappingfermionicrationalcftswiththreecharacters