One-instanton predictions of Seiberg-Witten curves for product groups

TL;DR

This paper derives one-instanton predictions for the prepotential in N=2 supersymmetric gauge theories with product gauge groups using a generalized perturbation expansion of Seiberg-Witten curves.

Contribution

It extends the systematic perturbation expansion method to product gauge groups with bifundamental matter, providing explicit one-instanton predictions.

Findings

Derived explicit one-instanton prepotential predictions.

Generalized perturbation expansion method for hyperelliptic curves.

Applicable to product gauge groups with bifundamental matter.

Abstract

One-instanton predictions for the prepotential are obtained from the Seiberg-Witten curve for the Coulomb branch of N=2 supersymmetric gauge theory for the product group \prod_{n=1}^{m} SU(N_n) with a massless matter hypermultiplet in the bifundamental representation (N_n,\bar N_{n+1}) of SU(N_n) x SU(N_{n+1}) for n=1 to m-1, together with N_0 and N_{m+1} matter hypermultiplets in the fundamental representations of SU(N_1) and SU(N_m) respectively. The derivation uses a generalization of the systematic perturbation expansion about a hyperelliptic curve developed by us in earlier work.