Confinement in 3d $\mathcal{N}=2$ $Spin(N)$ gauge theories with vector and spinor matters

TL;DR

This paper explores the different confinement phases in 3D $ abla=2$ $Spin(N)$ gauge theories with vector and spinor matter, highlighting how the Coulomb branch structure varies with gauge group rank and matter content.

Contribution

It provides a detailed analysis of the confinement phases and Coulomb branch structures in 3D $ abla=2$ $Spin(N)$ gauge theories with various matter representations, including the introduction of dressed operators.

Findings

Coulomb branch dimensions vary with gauge group and matter content.

In some cases, the Coulomb branch is three-dimensional, requiring dressed operators.

The quantum Coulomb branch structure is significantly affected by matter representations.

Abstract

We present various confinement phases of three-dimensional $\mathcal{N}=2$ $Spin(N)$ gauge theories with vector and spinor matters. The quantum Coulomb branch of the moduli space of vacua is drastically changed when the rank of the gauge group and the matter contents are changed. In many examples, the Coulomb branch is one- or two-dimensional but its interpretation varies. In some examples, the Coulomb branch becomes three-dimensional and we need to introduce a "dressed" Coulomb branch operator.