The instanton hunter's guide to supersymmetric SU( N) gauge theories

We present a compendium of results for ADHM multi-instantons in SU( N) SUSY gauge theories, followed by applications to N = 2 supersymmetric models. Extending recent SU(2) work, and treating the N = 1 and N = 2 cases in parallel, we construct: (i) the ADHM supermultiplet, (ii) the multi-instanton action, and (iii) the collective coordinate integration measure. Specializing to N = 2, we then give a closed formula for F _k, the k-instanton contribution to the prepotential, as a finite-dimensional collective coordinate integral. This amounts to a weak-coupling solution, in quadratures, of the low-energy dynamics of N = 2 SQCD, without appeal to duality. As an application, we calculate F ₁ for all SU( N) and any number of flavors N_F; for N_F < 2 N - 2 and N_F = 2 N - 1 we confirm previous instanton calculations and agree with the proposed hyper-elliptic curve solutions. For N_F = 2 N - 2 and N_F = 2 N with N > 3 we obtain new results, which in the latter case we do not understand how to reconcile with the curves.