One Instanton Predictions of a Seiberg-Witten curve from M-theory: the Symmetric Representation of SU(N)

TL;DR

This paper computes the one-instanton correction to the prepotential of N=2 SU(N) supersymmetric Yang-Mills theories with symmetric matter, using M-theory derived Seiberg-Witten curves, and confirms the results match known one-loop behavior.

Contribution

It provides the first calculation of the one-instanton correction for SU(N) theories with symmetric matter from M-theory curves, extending previous hyperelliptic curve methods.

Findings

One-instanton prepotential matches the expected one-loop result.

Perturbation expansion of the Seiberg-Witten differential yields correct instanton correction.

The approach confirms the validity of the M-theory derived curve for these theories.

Abstract

We consider N=2 supersymmetric Yang-Mills theories in four dimensions with gauge group SU(N) for N larger than two. 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 to be 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.