Built on

S. R. Coleman and B. Grossman, “’t Hooft’s Consistency Condition as a Consequence of Analyticity and Unitarity,” Nucl. Phys. B
1982
Earlier work this paper cites.
G. T. Horowitz, “Exactly Soluble Diffeomorphism Invariant Theories,” Commun. Math. Phys
1989
Earlier work this paper cites.
S. Elitzur, G. W. Moore, A. Schwimmer, and N. Seiberg, “Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory,” Nucl. Phys. B
1989
Earlier work this paper cites.
M. Atiyah, “Topological quantum field theories,” Inst. Hautes Etudes Sci. Publ. Math
1989
Earlier work this paper cites.
A. S. Cattaneo, P. Cotta-Ramusino, J. Frohlich, and M. Martellini, “Topological BF theories in three-dimensions and four-dimensions,” J. Math. Phys
1995
Earlier work this paper cites.
A. S. Cattaneo, P. Cotta-Ramusino, F. Fucito, M. Martellini, M. Rinaldi, A. Tanzini, and M. Zeni, “Four-dimensional Yang-Mills theory as a deformation of topological BF theory,” Commun. Math. Phys
1998
Earlier work this paper cites.
J. M. Maldacena, G. W. Moore, and N. Seiberg, “D-brane charges in five-brane backgrounds,” JHEP
2001
Earlier work this paper cites.
L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res
Original
2005
Earlier work this paper cites.
S. Gukov and E. Witten, “Rigid Surface Operators,” Adv. Theor. Math. Phys
Original
2010
Earlier work this paper cites.

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Then

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Later among the works it cites.
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Original
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Original
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2024

A SymTFT for Continuous Symmetries

Brennan, T. Daniel, Sun, Zhengdi

Understand

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.

Built on

S. R. Coleman and B. Grossman, “’t Hooft’s Consistency Condition as a Consequence of Analyticity and Unitarity,” Nucl. Phys. B
1982
Earlier work this paper cites.
G. T. Horowitz, “Exactly Soluble Diffeomorphism Invariant Theories,” Commun. Math. Phys
1989
Earlier work this paper cites.
S. Elitzur, G. W. Moore, A. Schwimmer, and N. Seiberg, “Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory,” Nucl. Phys. B
1989
Earlier work this paper cites.
M. Atiyah, “Topological quantum field theories,” Inst. Hautes Etudes Sci. Publ. Math
1989
Earlier work this paper cites.
A. S. Cattaneo, P. Cotta-Ramusino, J. Frohlich, and M. Martellini, “Topological BF theories in three-dimensions and four-dimensions,” J. Math. Phys
1995
Earlier work this paper cites.
A. S. Cattaneo, P. Cotta-Ramusino, F. Fucito, M. Martellini, M. Rinaldi, A. Tanzini, and M. Zeni, “Four-dimensional Yang-Mills theory as a deformation of topological BF theory,” Commun. Math. Phys
1998
Earlier work this paper cites.
J. M. Maldacena, G. W. Moore, and N. Seiberg, “D-brane charges in five-brane backgrounds,” JHEP
2001
Earlier work this paper cites.
L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res
Original
2005
Earlier work this paper cites.
S. Gukov and E. Witten, “Rigid Surface Operators,” Adv. Theor. Math. Phys
Original
2010
Earlier work this paper cites.