Abstract :
We investigate the large N limit of pure N=2 supersymmetric gauge theory with gauge group SU(N) by using the exact low energy effective action. Typical one-complex dimensional sections of the moduli space parametrized by a global complex mass scale v display three qualitatively different regions depending on the ratio between |v| and the dynamically generated scale Λ. At large |v|/Λ, instantons are exponentially suppressed as N→∞. When |v|∼Λ, singularities due to massless dyons occur. They are densely distributed in rings of calculable thicknesses in the v-plane. At small |v|/Λ, instantons disintegrate into fractional instantons of charge 1/(2N). These fractional instantons give non-trivial contributions to all orders of 1/N, unlike a planar diagrams expansion which generates a series in 1/N2, implying the presence of open strings. We have explicitly calculated the fractional instantons series in two representative examples, including the 1/N and 1/N2 corrections. Our most interesting finding is that the 1/N expansion breaks down at singularities on the moduli space due to severe infrared divergencies, a fact that has remarkable consequences.
