One-instanton predictions for non-hyperelliptic curves derived from M-theory

TL;DR

This paper derives one-instanton predictions for non-hyperelliptic Seiberg-Witten curves from M-theory, advancing understanding of supersymmetric gauge theories with complex gauge groups and matter representations.

Contribution

It introduces a systematic perturbation method and involution map techniques to analyze non-hyperelliptic curves from M-theory for N=2 supersymmetric gauge theories.

Findings

Derived one-instanton predictions for non-hyperelliptic curves.

Extended analysis to SU(N) theories with various matter representations.

Provided new computational tools for complex gauge theory curves.

Abstract

One-instanton predictions are obtained from certain non-hyperelliptic Seiberg-Witten curves derived from M-theory for N=2 supersymmetric gauge theories. We consider SU(N_1) x SU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with hypermultiplets in the defining representations of SU(N_1) and SU(N_2). We also consider SU(N) gauge theory with a hypermultiplet in the symmetric or antisymmetric representation, together with hypermultiplets in the defining representation. The systematic perturbation expansion about a hyperelliptic curve together with the judicious use of an involution map for the curve of the product groups provide the principal tools of the calculations.