Instanton Effects in Three-Dimensional Supersymmetric Gauge Theories with Matter

TL;DR

This paper computes instanton and perturbative effects on the Coulomb branch of 3D supersymmetric QCD with SU(2) gauge group, confirming and extending previous theoretical predictions about the moduli space and superpotential.

Contribution

It provides explicit calculations of instanton contributions, one-loop corrections, and superpotentials in 3D N=2 and N=4 supersymmetric gauge theories, confirming prior conjectures.

Findings

Coulomb branch matches Atiyah-Hitchin and Dancer's monopole moduli spaces.

One-loop corrections to the metric and complex structure are explicitly computed.

Superpotential including instanton effects is explicitly determined.

Abstract

Using standard field theory techniques we compute perturbative and instanton contributions to the Coulomb branch of three-dimensional supersymmetric QCD with N=2 and N=4 supersymmetry and gauge group SU(2). For the N=4 theory with one massless flavor, we confirm the proposal of Seiberg and Witten that the Coulomb branch is the double-cover of the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass term, we show that the asymptotic metric on the Coulomb branch coincides with the metric on Dancer's deformation of the monopole moduli space. For the N=2 theory with $N_f$ flavors, we compute the one-loop corrections to the metric and complex structure on the Coulomb branch. We then determine the superpotential including one-loop effects around the instanton background. These calculations provide an explicit check of several results previously obtained by symmetry and holomorphy arguments.