Dynamics of N=2 Supersymmetric Gauge Theories in Three Dimensions
Jan de Boer, Kentaro Hori, Yaron Oz
TL;DR
The paper analyzes three-dimensional N=2 supersymmetric gauge theories, focusing on the moduli spaces of vacua and non-perturbative superpotentials generated by monopole-instantons in weakly coupled regions. It develops a unified framework combining low-energy effective actions, duality, and one-loop metrics, and extends to general gauge groups and matter, with a detailed account for U($N_c$) and SU($N_c$) with $N_f$ flavors. Key results include the structure of quantum Coulomb/Higgs branches, explicit instanton-generated superpotentials, and the emergence of potential non-trivial N=2 superconformal fixed points at moduli-space singularities, all consistent with intersecting-brane pictures. The work provides a robust map between field theory, brane constructions, and index-theorem analyses, offering a comprehensive toolkit for exploring non-perturbative dynamics in 3d gauge theories.
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.