A SymTFT for continuous symmetries

A bstract 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...

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Bibliographic Details
Published in:The journal of high energy physics 2024-12, Vol.2024 (12), p.100-37
Main Authors: Brennan, T. Daniel, Sun, Zhengdi
Format: Article
Language:English
Subjects:
Anomalies in Field and String Theories
Boundary conditions
Classical and Quantum Gravitation
Elementary Particles
Global Symmetries
Lie groups
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Symmetry
Topological Field Theories
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Summary:A bstract 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 d QFTs, describe the ℚ / ℤ non-invertible chiral symmetry in 4 d theories, and conjecture the SymTFT for general continuous G (0) global symmetries.
ISSN:1029-8479
DOI:10.1007/JHEP12(2024)100