Superconformal Index for $\mathcal{N}=3$ $\hat{ADE}$ Chern-Simons Quiver Gauge Theories

TL;DR

This paper computes superconformal indices for a class of $ =3$ $ ext{ADE}$ Chern-Simons quiver gauge theories using localization, providing insights into their large $N$ behavior and dual M-theory descriptions.

Contribution

It introduces a method to compute superconformal indices for $ =3$ $ ext{ADE}$ quiver theories, including non-zero magnetic flux sectors, and analyzes their large $N$ limit.

Findings

Superconformal indices computed for $ =3$ $ ext{ADE}$ theories.

Large $N$ analysis reveals index behavior and dualities.

Inclusion of magnetic flux sectors enhances the index's completeness.

Abstract

We compute superconformal indices for $\mathcal{N} = 3$ $\hat{ADE}$ Chern-Simons quiver gauge theories with a product gauge group $\prod_i U(N)_i$, using the method of supersymmetric localization. We also perform a large $N$ analysis of the index. This index includes contribution from non zero magnetic flux sector. The fact that these theories have a weakly coupled UV completion in terms of $\mathcal{N}= 3$ supersymmetric Chern-Simons Yang-Mills theories enables us to apply the localization technique. Such theories have dual M-theory description on $\mathrm{AdS}_4\times M_7$, where $M_7$ is a tri-Sasaki Einstein manifold.