One-Instanton Test of a Seiberg–Witten Curve from M-theory: the Antisymmetric Representation of SU(N)

One-instanton predictions are obtained from the Seiberg–Witten curve derived from M-theory by Landsteiner and Lopez for the Coulomb branch of N = 2 supersymmetric SU(N) gauge theory with a matter hypermultiplet in the antisymmetric representation. Since this cubic curve describes a Riemann surface that is non-hyperelliptic, a systematic perturbation expansion about a hyperelliptic curve is developed, with a comparable expansion for the Seiberg–Witten differential. Calculation of the period integrals of the SW differential by the method of residues of D’Hoker, Krichever, and Phong enables us to compute the prepotential explicitly to one-instanton order. It is shown that the one-instanton predictions for SU(2), SU(3), and SU(4) agree with previously available results. For SU(N), N ≥ 5, our analysis provides explicit predictions of a curve derived from M-theory at the one-instanton level in field theory.