On the quantum moduli space of vacua of N=2 supersymmetric gauge theories

Families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of N = 2 supersymmetric SO(N-c) gauge theories coupled to N-f flavors of quarks in the vector representation are constructed. The quantum moduli spaces for 2N(f) < N-c-1 are determined completely by imposing R-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue calculations. The quantum moduli spaces for 2N(f) greater than or equal to N-c-1 theories are parameterized and their general structure is worked out using residue calculations. The exact metrics on the quantum moduli spaces as well as the exact spectrum of stable massive states are derived. The results presented here together with recent results of Martinec and Warner provide a natural conjecture for the form of the curves for the other gauge groups.