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

TL;DR

This paper derives one-instanton predictions for N=2 supersymmetric SU(N) gauge theories with antisymmetric matter from a non-hyperelliptic Seiberg-Witten curve obtained via M-theory, extending known results to higher N.

Contribution

It develops a systematic perturbation method for non-hyperelliptic curves and explicitly computes the prepotential at one-instanton order for SU(N) theories, including N > 4.

Findings

Agreement with known results for SU(2), SU(3), and SU(4)

Explicit predictions for SU(N) with N > 4

Method for computing period integrals of non-hyperelliptic curves

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.