One-instanton predictions of a seiberg-witten curve from M theory: The symmetric representation of SU(N)

Isabel P. Ennes, Brandeis University
Henric Rhedin, Brandeis University
Stephen G. Naculich, Bowdoin College
Howard J. Schnitzer, Brandeis University

Abstract

We consider N = 2 supersymmetric Yang-Mills theories in four dimensions with gauge group SU(N) for N larger than 2. Using the cubic curve for a matter hypermultiplet transforming in the symmetric representation, obtained from M theory by Landsteiner and Lopez, we calculate the prepotential up to the one-instanton correction. We treat the curve as being approximately hyperelliptic and perform a perturbation expansion for the Seiberg-Witten differential to get the one-instanton contribution. We find that it reproduces the correct result for one loop, and we obtain the prediction for that curve for the one-instanton correction term.