Spectral curves for super-Yang-Mills with adjoint hypermultiplet for general simple Lie algebras Original Research Article

The Seiberg-Witten curves and differentials for N = 2 supersymmetric Yang-Mills theories with one hypermultiplet of mass m in the adjoint representation of the gauge algebra G, are constructed for arbitrary classical or exceptional simple G (except G2. The curves are obtained from the recently established Lax pairs with spectral parameter for the (twisted) elliptic Calogero-Moser integrable systems associated with the algebra G. Curves and differentials are shown to have the proper group theoretic and complex analytic structure, and to behave as expected when m tends either to 0 or to oo. By way of example, the prepotential for G = SU (N) evaluated with these techniques, is shown to agree with standard perturbative results. A renormalization group type equation relating the prepotential to the Calogero-Moser Hamiltonian is obtained for arbitrary G, generalizing a previous result for G = SU(N). Duality properties and decoupling to theories with other representations are briefly discussed.