Testing Seiberg–Witten theory to all orders in the instanton expansion

Abstract

In the context of softly-broken N=4 to N=2 supersymmetric SU( N) gauge theory, we calculate using semi-classical instanton methods, the lowest order non-trivial terms in the mass expansion of the prepotential for all instanton number. We find exact agreement with Seiberg–Witten theory and thereby achieve the most powerful test yet of this theory. We also calculate the one- and two-instanton contributions completely and also find consistency with Seiberg–Witten theory. Our approach relies on the fact that the instanton calculus admits a nilpotent fermionic symmetry, or BRST operator, whose existence implies that the integrals over the instanton moduli space, which give the coefficients of the prepotential, localize on the space of resolved point-like instantons or what we call “topicons”.