On N = 2 supersymmetric QCD with four flavors Original Research Article

Seiberg and Wittenʹs proposed solution of N = 2 SQCD with Nc = 2 and NF = 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 τeff(0) and ũ rather than τ and u = 〈Tr A2〉. SL(2,Z) invariance of the curve is preserved. However, there is now an infinite ambiguity in the relation between τeff(0) and τ and between ũ and u, corresponding to an infinite number of unknown coefficients in the instanton expansion. Thus the reinterpreted curve (unlike the cases NF < 4) no longer determines the quantum modulus u as a function of the classical VEV a.