Low-Energy Dynamics of 3d $\mathcal{N}=2$ $G_2$ Supersymmetric Gauge Theory

TL;DR

This paper explores the low-energy behavior of 3d $ abla=2$ supersymmetric $G_2$ gauge theories, revealing how monopole effects shape the moduli space and lead to different phases depending on matter content.

Contribution

It provides a detailed analysis of the quantum Coulomb branch and phase structure of 3d $ abla=2$ $G_2$ gauge theories with matter, including superconformal index checks.

Findings

Quantum Coulomb branch is one-dimensional due to monopole effects.

Various phases like s-confinement or Coulomb-Higgs merging depend on matter content.

Superconformal indices support the phase structure analysis.

Abstract

We study a three-dimensional $\mathcal{N}=2$ supersymmetric $G_2$ gauge theory with and without fundamental matters. We find that a classical Coulomb branch of the moduli space of vacua is partly lifted by monopole-instantons and the quantum Coulomb moduli space would be described by a complex one-dimensional space. Depending on the number of the matters in a fundamental representation, the low-energy dynamics of the theory shows various phases like s-confinement or quantum merging of the Coulomb and the Higgs branches. We also investigate superconformal indices as an independent check of our analysis.