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 d erived from M-theory by Landsteiner and Lopez for the Coulomb branch o f 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 perturbatio n expansion about a hyperelliptic curve is developed, with a comparabl e expansion for the Seiberg-Witten differential. Calculation of the pe riod integrals of the SW differential by the method of residues of D'H oker, Krichever, and Phong enables us to compute the prepotential expl icitly to one-instanton order. It is shown that the one-instanton pred ictions for SU(2), SU(3), and SU(4) agree with previously available re sults. For SU(N), N is greater than or equal to 5, our analysis provid es explicit predictions of a curve derived from M-theory at the one-in stanton level in field theory. (C) 1998 Elsevier Science B.V.