Duality symmetries for N = 2 supersymmetric QCD with vanishing β-functions Original Research Article

We construct the duality groups for N = 2 supersymmetric QCD with gauge group SU(2n + 1) and Nf = 4n + 2 hypermultiplets in the fundamental representation. The groups are generated by two elements S and T that satisfy a relation (STS−1T)2n+1 = 1. Thus, the groups are not subgroups of SL(2, Z) We also construct automorphic functions that map the fundamental region of the group generated by T and STS to the Riemann sphere. These automorphic functions faithfully represent the duality symmetry in the Seiberg-Witten curve.