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

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Dunajski, Maciej¹  Hoegner, Moritz¹ 

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England

关键词: Instantons;    Self-duality equations;    Spin(7);   

DOI  :  10.1016/j.geomphys.2012.03.013

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free