Orbifold instantons, moment maps, and Yang-Mills theory with sources

Abstract

We revisit the problem of constructing instantons on ADE orbifolds R4/Γ and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R4/Γ which are BPS equations for the Yang-Mills equations with an external current. The relation between level sets of the moment maps in the hyper-Kähler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically symmetric Γ-equivariant connections on complex V bundles over R4/Γ which are tailored to the way in which the orbifold group acts on the fibers. Some explicit Abelian and non-Abelian SU(2)-invariant solutions to the instanton equations on the orbifold are worked out. © 2013 American Physical Society.