On N=2 Supersymmetric QCD with 4 Flavors

TL;DR

This paper resolves discrepancies in the Seiberg-Witten solution for N=2 SQCD with four flavors by reparametrizing the elliptic curve, preserving SL(2,Z) invariance but introducing an infinite ambiguity in key relations.

Contribution

It introduces a reparametrization of the elliptic curve that resolves known conflicts with instanton calculations in N=2 SQCD with four flavors.

Findings

Discrepancies with instanton calculations are resolved.

SL(2,Z) invariance of the elliptic curve is maintained.

Infinite ambiguity arises in the relation between parameters.

Abstract

Seiberg and Witten's proposed solution of N=2 SQCD with N_c=2 and N_F=4 is known to conflict with instanton calculations in three distinct ways. Here we show how to resolve all three discrepancies, simply by reparametrizing the elliptic curve in terms of quantities $\tau^0_{eff}$ and $\tilde{u}$ rather than $\tau$ and $u = < Tr A^2 > $. SL(2,Z) invariance of the curve is preserved. However, there is now an infinite ambiguity in the relation between $\tau^0_{eff}$ and $\tau$ and between $\tilde{u}$ and $u$, corresponding to an infinite number of unknown coefficients in the instanton expansion. Thus the reinterpreted curve (unlike the cases N_F<4) no longer determines the quantum modulus u as a function of the classical VEV a.