Multi-instanton calculus inN=2supersymmetric gauge theory

The Seiberg-Witten solution of $N=2\mathrm{}$ supersymmetric SU(2) gauge theory may be viewed as a prediction for the infinite family of constants {${\mathcal{F}}_n$} measuring the $n$-instanton contribution to the prepotential $\mathcal{F}$. Here we examine the instanton physics directly, in particular the contribution of the general self-dual solution of topological charge $n$ constructed by Atiyah, Drinfeld, Hitchin, and Manin (ADHM). In both the bosonic and supersymmetric cases, we determine both the large- and short-distance behavior of all the fields in this background. This allows us to construct the exact classical interaction between $n$ ADHM (super)instantons mediated by the adjoint Higgs bosons. We calculate the one- and two-instanton contributions to the low-energy Seiberg-Witten effective action and find precise agreement with their predicted values of ${\mathcal{F}}_1$ and ${\mathcal{F}}_2$.