{"title":"Fermionic and parafermionic CFTs with \\( \\hat{su}(2) \\) and \\( \\hat{su}(3) \\) symmetry","authors":"Kohki Kawabata","doi":"10.1007/JHEP02(2025)070","DOIUrl":null,"url":null,"abstract":"<p>We investigate two-dimensional conformal field theories (CFTs) with affine <span>\\( \\hat{su}(2) \\)</span> and <span>\\( \\hat{su}(3) \\)</span> algebra symmetry. Their bosonic modular-invariant partition functions have been fully classified based on the ADE classification. In this work, we extend the classification to include fermionic and parafermionic CFTs with the same affine symmetries, utilizing techniques of fermionization and parafermionization. We find that the fermionic and parafermionic <span>\\( \\hat{su}(2) \\)</span> models are related to non-simply laced Dynkin diagrams.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2025 2","pages":""},"PeriodicalIF":5.5000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP02(2025)070.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of High Energy Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/JHEP02(2025)070","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate two-dimensional conformal field theories (CFTs) with affine \( \hat{su}(2) \) and \( \hat{su}(3) \) algebra symmetry. Their bosonic modular-invariant partition functions have been fully classified based on the ADE classification. In this work, we extend the classification to include fermionic and parafermionic CFTs with the same affine symmetries, utilizing techniques of fermionization and parafermionization. We find that the fermionic and parafermionic \( \hat{su}(2) \) models are related to non-simply laced Dynkin diagrams.
期刊介绍：
The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal.
Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles.
JHEP presently encompasses the following areas of theoretical and experimental physics:
Collider Physics
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General Relativity and Gravitation
Supersymmetry
Mathematical Methods of Physics
Mostly Solvable Models
Astroparticles
Statistical Field Theories
Mostly Weak Interactions
Mostly Strong Interactions
Quantum Field Theory (phenomenology)
Strings and Branes
Phenomenological Aspects of Supersymmetry
Mostly Strong Interactions (phenomenology).
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