SU(2) solutions to self-duality equations in eight dimensions

We consider the octonionic self-duality equations on eight-dimensional manifolds of the form M-8 = M-4 x R-4, where M-4 is a hyper-Kahler four-manifold. We construct explicit solutions to these equations and their symmetry reductions to the non-abelian Seiberg-Witten equations on M-4 in the case when the gauge group is SU(2). These solutions are singular for flat and Eguchi-Hanson backgrounds. For M-4 = R x g, with a cohomogeneity one hyper-Kahler metric, where g. is a nilpotent (Bianchi II) Lie group, we find a solution which is singular only on a single-sided domain wall. This gives rise to a regular solution of the non-abelian Seiberg-Witten equations on a four-dimensional nilpotent Lie group which carries a regular conformally hyper-Kahler metric. (C) 2012 Elsevier B.V. All rights reserved.