Periods and Prepotential of N=2 SU(2) Supersymmetric Yang-Mills Theory with Massive Hypermultiplets

TL;DR

This paper derives a simple formula for the periods and prepotential of N=2 SU(2) supersymmetric Yang-Mills theory with massive hypermultiplets, using hypergeometric functions to analyze weak and strong coupling regimes.

Contribution

It introduces a new explicit integral formula for the periods involving hypergeometric functions, applicable to theories with massive hypermultiplets and conformal points.

Findings

Explicit formulas for periods using hypergeometric functions.

Prepotential calculations in both weak and strong coupling regions.

Expression of Higgs and dual fields as hypergeometric functions at conformal points.

Abstract

We derive a simple formula for the periods associated with the low energy effective action of $N=2$ supersymmetric $SU(2)$ Yang-Mills theory with massive $N_f\le 3$ hypermultiplets. This is given by evaluating explicitly the integral associated to the elliptic curve using various identities of hypergeometric functions. Following this formalism, we can calculate the prepotential with massive hypermultiplets both in the weak coupling region and in the strong coupling region. In particular, we show how the Higgs field and its dual field are expressed as generalized hypergeometric functions when the theory has a conformal point.