Left chiral “zero modes” in a super-self-dual Yang-Mills background

Abstract

A super-self-duality constraint can be imposed on the curvature two-form in supersymmetric Yang-Mills theories formulated in euclidean superspace. If left covariantly chiral superfields are coupled to such a background, part of this space of superfields is annihilated by a superspace operator constructed from the quadratic part of the action. These are analogous to the zero modes of the Dirac equation which occur in the presence of a multi-instanton. Using the supersymmetric version of the ADHM formalism, this space of left covariantly chiral “zero mode” superfields is constructed in the fundamental representation of an SU( n) gauge group. It is shown to be spanned by a set of k superfields, where k is the instanton number of the bosonic component of the Yang-Mills background.