M and F-Theory Instantons, N=1 Supersymmetry and Fractional Topological Charges

TL;DR

This paper explores how instanton effects generate superpotentials in three-dimensional N=2 supersymmetric gauge theories derived from four-dimensional theories, revealing connections to fractional instantons and Coulomb branch singularities.

Contribution

It provides a detailed analysis of instanton-generated superpotentials in compactified theories, highlighting the role of fractional topological charges and Coulomb branch singularities.

Findings

Vacua correspond to Coulomb branch singularities in the decompactification limit.

Fractional instantons contribute to the superpotential in pure gauge theories.

The study extends understanding of instanton effects in lower-dimensional supersymmetric theories.

Abstract

We analize instanton generated superpotentials for three dimensional N=2 supersymmetric gauge theories obtained by compactifying on S^1 N=1 four dimensional theories. In the N_f=1 case, we find that the vacua in the decompactification limit is given by the singular points of the Coulomb branch of the N=2 four dimensional theory (we also consider the massive case). The decompactification limit of the superpotential for pure gauge theories without chiral matter is interpreted in terms of `t Hooft's fractional instanton amplitudes.