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

Families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of N = 2 supersymmetric SO(Nc) gauge theories coupled to Nf flavors of quarks in the vector representation are constructed. The quantum moduli spaces for 2Nf < Nc − 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 2Nf ⩾ Nc − 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.