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SU(2) solutions to self-duality equations in eight dimensions | | Maciej Dunajski
; Moritz Hoegner
; | | Date: |
21 Sep 2011 | | Abstract: | We consider the octonionic self-duality equations on eight-dimensional
manifolds of the form $M_8=M_4 imes R^4$, where $M_4$ is a hyper-K"ahler
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 $M_4=R imes {mathcal G}$ with a cohomogeneity
one hyper-K"ahler metric, where ${mathcal G}$ 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-K"ahler metric. | | Source: | arXiv, 1109.4537 | | Services: | Forum | Review | PDF | Favorites | |
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