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Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices (2210.02466v3)

Published 5 Oct 2022 in hep-th

Abstract: Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete zero-form global symmetries, and possibly a one-form symmetry, in 3d $\mathcal{N} \geq 3$ gauge theories using the superconformal index. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, such as the $\mathrm{U}(1)k$ gauge theory with hypermultiplets of diverse charges, the $T(\mathrm{SU}(N))$ theory of Gaiotto-Witten, the theories with $\mathfrak{so}(2N){2k}$ gauge algebra and hypermultiplets in the vector representation, and variants of the Aharony-Bergman-Jafferis (ABJ) theory with the orthosymplectic gauge algebra. Gauging appropriate global symmetries of some of these models, we obtain various interesting theories with non-invertible symmetries or two-group structures.

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