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

TL;DR

This paper investigates 3d $ ext{SCFTs}$ with $ ext{N}=3$ Chern-Simons theories coupled to $T_N$ theories, revealing conditions for supersymmetry enhancement and analyzing their one-form symmetries and moduli spaces.

Contribution

It identifies new conditions under which these theories flow to $ ext{N} extgreater=4$ supersymmetric SCFTs and analyzes their symmetry anomalies and moduli space geometries.

Findings

Supersymmetry can enhance to $ ext{N}=6$ under specific level conditions.

Existence of infinite families flowing to $ ext{N}=4$ SCFTs without the level condition.

Decoupled topological sectors are present in the infrared.

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 $4 \leq \mathcal{N} \leq 6$ 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 $\mathcal{N} \geq 4$ 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.