The Prepotential of N=2 SU(2) x SU(2) Supersymmetric Yang-Mills Theory with Bifundamental Matter

TL;DR

This paper investigates the non-perturbative effective action of N=2 SU(2) x SU(2) supersymmetric Yang-Mills theory with bifundamental matter, deriving the exact prepotential using hyperelliptic curves and analyzing parameter dependencies.

Contribution

It provides the exact holomorphic prepotential for the theory with bifundamental matter using hyperelliptic curves, expanding understanding of non-perturbative effects.

Findings

Derived the periods and prepotential from hyperelliptic curves.

Analyzed the dependence of the solution on the parameter q.

Explored properties of the effective action in weak coupling.

Abstract

We study the non-perturbative, instanton-corrected effective action of the N=2 SU(2) x SU(2) supersymmetric Yang-Mills theory with a massless hypermultiplet in the bifundamental representation. Starting from the appropriate hyperelliptic curve, we determine the periods and the exact holomorphic prepotential in a certain weak coupling expansion. We discuss the dependence of the solution on the parameter q=L2^2/L1^2 and several other interesting properties.