Multi-instanton calculus in N=2 supersymmetric gauge theory. II. Coupling to matter.

Abstract

We further discuss the $N=2$ superinstantons in SU(2) gauge theory, obtained from the general self-dual solutions of topological charge $n$ constructed by Atiyah, Drinfeld, Hitchin, and Manin (ADHM). We realize the $N=2$ supersymmetry algebra as actions on the superinstanton moduli. This allows us to recast in concise superfield notation our previously obtained expression for the exact classical interaction between $n$ ADHM superinstantons mediated by the adjoint Higgs bosons, and, moreover, to incorporate ${N}_{F}$ flavors of hypermultiplets. We perform explicit one- and two-instanton checks of the Seiberg-Witten prepotentials for all ${N}_{F}$ and arbitrary hypermultiplet masses. Our results for the low-energy couplings are all in precise agreement with the predictions of Seiberg and Witten except for ${N}_{F}=4$, where we find a finite renormalization of the coupling which is absent in the proposed solution.