Dynamics of N=2 Supersymmetric Gauge Theories in Three Dimensions

TL;DR

This paper analyzes the moduli spaces and superpotentials of three-dimensional N=2 supersymmetric gauge theories, revealing their quantum structures, superconformal points, and consistency with string theory brane models.

Contribution

It provides exact superpotentials and quantum moduli space descriptions for N=2 theories with various gauge groups and matter, including non-trivial superconformal points.

Findings

Exact superpotentials computed for U(N_c) and SU(N_c) gauge groups.

Identification of superconformal field theory candidates at moduli space singularities.

Agreement between field theory results and intersecting brane configurations.

Abstract

We study the structure of the moduli spaces of vacua and superpotentials of N=2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N=2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N_f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.