A SymTFT for Continuous Symmetries

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 $\mathbb{Q}/\mathbb{Z}$ non-invertible chiral symmetry in $4d$ theories, and conjecture the SymTFT for general continuous $G^{(0)}$ global symmetries.

36 pages, 5 figures

Cited by in corpus (4)

• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond