Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.

On the symmetry TFT of Yang-Mills-Chern-Simons theory / Argurio, Riccardo; Benini, Francesco; Bertolini, Matteo; Galati, Giovanni; Niro, Pierluigi. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2024:7(2024). [10.1007/JHEP07(2024)130]

On the symmetry TFT of Yang-Mills-Chern-Simons theory

Riccardo Argurio;Francesco Benini;Matteo Bertolini
;
Giovanni Galati;Pierluigi Niro
2024-01-01

Abstract

Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.
2024
2024
7
130
10.1007/JHEP07(2024)130
https://arxiv.org/abs/2404.06601
Argurio, Riccardo; Benini, Francesco; Bertolini, Matteo; Galati, Giovanni; Niro, Pierluigi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/140350
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