The large N limit of N=2 super Yang-Mills, fractional instantons and infrared divergences

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 upsilon display three qualitatively different regions depending on the ratio between \ upsilon \ and the dynamically generated scale Lambda. At large \ upsilon \/Lambda, instantons are exponentially suppressed as N --> infinity. When \ upsilon \ similar to Lambda, singularities due to massless dyons occur. They are densely distributed in rings of calculable thicknesses in the upsilon -plane. At small \ upsilon \/Lambda, 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/N-2, implying the presence of open strings. We have explicitly calculated the fractional instantons series in two representative examples, including the 1/N and 1/N-2 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, (C) 2001 Published by Elsevier Science B.V.