Hyperelliptic curves for Supersymmetric Yang-Mills

TL;DR

This paper constructs and analyzes the hyperelliptic curve for N=2 SU(3) super Yang-Mills theory with six flavors, exploring its duality properties and differences from previous results.

Contribution

It provides a new explicit construction of the hyperelliptic curve for the SU(3) theory using genus two theta functions and discusses its duality properties.

Findings

Constructed the hyperelliptic curve for the theory.

Identified a duality subgroup not isomorphic to Sp(2,Z).

Presented results differing from previous studies.

Abstract

In this paper we discuss the hyperelliptic curve for $N=2$ $SU(3)$ super Yang-Mills with six flavors of hypermultiplets. We start with a generic genus two surface and construct the curve in terms of genus two theta functions. From this one can construct the curve for $m_i=u=0$. This curve is explicitly dual under a subgroup of $Sp(4,Z)$ which is not isomorphic to $Sp(2,Z)$. We then proceed to construct the curve for the general $SU(3)$ theory and discuss the duality properties of the theory. The results given here differ from those given previously.