Instantons, three dimensional gauge theories, and monopole moduli spaces

Abstract

We calculate instanton corrections to three dimensional gauge theories with $N=4$ and $N=8$ supersymmetry and $\mathrm{SU}(n)$ gauge groups. The $N=4$ results give new information about the moduli space of $n$ BPS $\mathrm{SU}(2)$ monopoles, including the leading order non-pairwise interaction terms. A few comments are made on the relationship of the $N=8$ results to membrane scattering in matrix theory.