One-Instanton Test of a Seiberg-Witten Curve from M-theory: the Antisymmetric Representation of SU(N)
Stephen G. Naculich, Henric Rhedin, Howard J. Schnitzer
Abstract
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 > 4, our analysis provides explicit predictions of a curve derived from M-theory at the one-instanton level in field theory.