Integrable structure in supersymmetric gauge theories with massive hypermultiplets

We study the quantum moduli space of vacua of N = 2 supersymmetric SU(Nc) gauge theories coupled to Nf flavors of quarks in the fundamental representation. We identify the moduli space of the Nc = 3 and Nf = 2 massless case with the full spectral curve obtained from the Lax representation of the Goryachev-Chaplygin top. For the case with massive quarks, we present an integrable system where the corresponding hyperelliptic curve parametrizing the Laurent solution coincides with that of the moduli space of Nc = 3 with Nf = 0, 1, 2. We discuss possible generalizations of the integrable systems relevant to gauge theories with Nc ≠ 3 and general Nf.