Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices

TL;DR

This paper investigates mixed anomalies, non-invertible symmetries, and two-group structures in 3d superconformal gauge theories using the superconformal index, revealing new constraints and symmetries in these quantum field theories.

Contribution

It introduces a method to analyze mixed anomalies and symmetries in 3d $ ext{SCFT}$s via superconformal indices, including non-invertible and two-group symmetries, across various gauge theories.

Findings

Demonstrates the effectiveness of superconformal index in detecting anomalies.

Identifies non-invertible symmetries in certain gauge theories.

Constructs theories with two-group structures through gauging global symmetries.

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.