Chern-Simons-Trinion Theories: One-form Symmetries and Superconformal Indices

Abstract

We study 3d theories containing $\mathcal{N}=3$ Chern-Simons vector multiplets coupled to the $\mathrm{SU}(N{)}^3$ flavour symmetry of 3d $T_N$ theories with Chern-Simons level $k_1$, $k_2$ and $k_3$. It was formerly pointed out that these theories flow to infrared SCFTs with enhanced $\mathcal{N}=4$ supersymmetry when $1/k_1+1/k_2+1/k_3=0$. We examine superconformal indices of these theories which reveal that supersymmetry of the infrared SCFTs may get enhanced to $4\le \mathcal{N}\le 6$ if such a condition is satisfied. Moreover, even if the Chern-Simons levels do not obey the aforementioned condition, we find that there is still an infinite family of theories that flows to infrared SCFTs with $\mathcal{N}=4$ supersymmetry. The 't Hooft anomalies of the one-form symmetries of these theories are analysed. As a by-product, we observe that there is generally a decoupled topological sector in the infrared. When the infrared SCFTs have $\mathcal{N}\ge 4$ supersymmetry, we also study the Higgs and Coulomb branch limits of the indices which provide geometric information of the moduli space of the theories in question in terms of the Hilbert series.

51 pages with a number of figures. Version 2: published in the JHEP. Version 3: comments added

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