N = 2 supersymmetric Yang-Mills theories for all classical gauge groups, that is, for SU (N), SO(N), and Sp(N) is considered. The formal expression for almost all models accepted by the asymptotic freedom are obtained. The equations which define the Seiberg-Witten curve are proposed. In some cases they are solved. It is shown that for all considered the… (More)
We solve N = 2 supersymmetric Yang-Mills theories for arbitrary classical gauge group, i.e. SU (N), SO(N), Sp(N). In particular, we derive the prepotential of the low-energy effective theory, and the corresponding Seiberg-Witten curves. We manage to do this without resolving singularities of the compactified instanton moduli spaces.
N = 2 supersymmetric Yang-Mills theories for all classical gauge groups, that is, for SU (N), SO(N), and Sp(N) is considered. The equations which define the Seiberg-Witten curve are proposed. In some cases they are solved. It is shown that for (almost) all models allowed by the asymptotic freedom the 1-instanton corrections which follows from these… (More)
We investigate the possibility to extract Seiberg-Witten curves from the formal series for the prepotential, which was obtained by the Nekrasov approach. A method for models whose Seiberg-Witten curves are not hyperelliptic is proposed. It is applied to the SU(N) model with one symmetric or antisymmetric representations as well as for SU(N 1) × SU(N 2)… (More)
We apply equivariant integration technique, developed in the context of instanton counting, to two dimensional N = 2 supersymmetric Yang–Mills models. Twisted superpotential for U(N) model is computed. Connections to the four dimensional case are discussed. Also we make some comments about the eight dimensional model which manifests similar features.
The non-perturbative behavior of the N = 2 supersymmetric Yang–Mills theories is both highly non-trivial and tractable. In the last three years the valuable progress was achieved in the instanton counting, the direct evaluation of the low-energy effective Wilsonian action of the theory. The localization technique together with the Lorentz deformation of the… (More)
We show that the solitonic contribution of toroidally compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of compactification on a circle, the Hamiltonian is the Laplacian on the 2g-dimensional Jacobian torus associated with the genus g Riemann surface… (More)