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

We revisit the problem of constructing instantons on ADE orbifolds R-4/Gamma and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R-4/Gamma 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-Kahler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically symmetric Gamma-equivariant connections on complex V bundles over R-4/Gamma 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.