July 15, 2024 | Riccardo Argurio, Francesco Benini, Matteo Bertolini, Giovanni Galati and Pierluigi Niro
The paper explores the Symmetry Topological Field Theory (Symmetry TFT) of three-dimensional Yang-Mills-Chern-Simons (YM-CS) theories, focusing on the $\mathfrak{su}(N)_k$ gauge algebra. The main challenges arise from the non-trivial braiding of one-form symmetry defects, which are charged under the same symmetry they generate, leading to anomalies. These anomalies pose puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. The authors propose that these puzzles can be resolved by including "endable" (tubular) surfaces in the class of bulk topological operators. This approach allows for the reproduction of all global variants of the theory, including their symmetries and anomalies. The validity of this proposal is verified through a top-down holographic realization of the same class of theories in type IIB string theory. The holographic model, based on D3/D7-branes, is used to extract the topological sector and verify the Symmetry TFT, providing an independent check of the field theory analysis. The results also support the claim that the holographic model captures the evolution of line operators from being topological to non-topological in the deep infrared, where the full non-invertible 1-form symmetry of pure Chern-Simons theory is realized.The paper explores the Symmetry Topological Field Theory (Symmetry TFT) of three-dimensional Yang-Mills-Chern-Simons (YM-CS) theories, focusing on the $\mathfrak{su}(N)_k$ gauge algebra. The main challenges arise from the non-trivial braiding of one-form symmetry defects, which are charged under the same symmetry they generate, leading to anomalies. These anomalies pose puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. The authors propose that these puzzles can be resolved by including "endable" (tubular) surfaces in the class of bulk topological operators. This approach allows for the reproduction of all global variants of the theory, including their symmetries and anomalies. The validity of this proposal is verified through a top-down holographic realization of the same class of theories in type IIB string theory. The holographic model, based on D3/D7-branes, is used to extract the topological sector and verify the Symmetry TFT, providing an independent check of the field theory analysis. The results also support the claim that the holographic model captures the evolution of line operators from being topological to non-topological in the deep infrared, where the full non-invertible 1-form symmetry of pure Chern-Simons theory is realized.