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

TL;DR

This paper explores the large Nc limit of N=2 super Yang-Mills theory, revealing fractional instantons, infrared divergences at singularities, and implications for open string contributions in the theory.

Contribution

It uncovers the role of fractional instantons and infrared divergences in the large Nc limit of N=2 super Yang-Mills, highlighting breakdowns of the 1/N expansion at singularities.

Findings

Fractional instantons contribute to all orders of 1/N.

Infrared divergences cause the 1/N expansion to break down at singularities.

Explicit calculations of fractional instanton series in key examples.

Abstract

We investigate the large Nc limit of pure N=2 supersymmetric gauge theory with gauge group SU(Nc) 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 Lambda. At large |v|/Lambda, instantons are exponentially suppressed as N goes to infinity. When |v| is of order Lambda, singularities due to massless dyons occur. They are densely distributed in rings of calculable thicknesses in the v-plane. At small |v|/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.