{"title":"A SymTFT for continuous symmetries","authors":"T. Daniel Brennan, Zhengdi Sun","doi":"10.1007/JHEP12(2024)100","DOIUrl":null,"url":null,"abstract":"<p>Symmetry is a powerful tool for studying dynamics in QFT: it provides selection rules, constrains RG flows, and often simplifies analysis. Currently, our understanding is that the most general form of symmetry is described by categorical symmetries which can be realized via Symmetry TQFTs or “SymTFTs”. In this paper, we show how the framework of the SymTFT, which is understood for discrete symmetries (i.e. finite categorical symmetries), can be generalized to continuous symmetries. In addition to demonstrating how U(1) global symmetries can be incorporated into the paradigm of the SymTFT, we apply our formalism to study cubic U(1) anomalies in 4<i>d</i> QFTs, describe the <i>ℚ</i>/<i>ℤ</i> non-invertible chiral symmetry in 4<i>d</i> theories, and conjecture the SymTFT for general continuous <i>G</i><sup>(0)</sup> global symmetries.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":"2024 12","pages":""},"PeriodicalIF":5.4000,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/JHEP12(2024)100.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/JHEP12(2024)100","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
Symmetry is a powerful tool for studying dynamics in QFT: it provides selection rules, constrains RG flows, and often simplifies analysis. Currently, our understanding is that the most general form of symmetry is described by categorical symmetries which can be realized via Symmetry TQFTs or “SymTFTs”. In this paper, we show how the framework of the SymTFT, which is understood for discrete symmetries (i.e. finite categorical symmetries), can be generalized to continuous symmetries. In addition to demonstrating how U(1) global symmetries can be incorporated into the paradigm of the SymTFT, we apply our formalism to study cubic U(1) anomalies in 4d QFTs, describe the ℚ/ℤ non-invertible chiral symmetry in 4d theories, and conjecture the SymTFT for general continuous G(0) global symmetries.
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
Underground and Large Array Physics
Quantum Field Theory
Gauge Field Theories
Symmetries
String and Brane Theory
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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