Octonionic Yang-Mills Instanton on Quaternionic Line Bundle of Spin(7) Holonomy

Abstract

The total space of the spinor bundle on the four dimensional sphere S4 is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang-Mills instanton on this eight dimensional gravitational instanton. This is a higher dimensional generalization of (anti-)self-dual instanton on the Eguchi-Hanson space. We propose an ansatz for Spin(7) Yang-Mills field and derive a system of non-linear ordinary differential equations. The solutions are classified according to the asymptotic behavior at infinity. We give a complete solution, when the gauge group is reduced to a product of SU(2) subalgebras in Spin(7). The existence of more general Spin(7) valued solutions can be seen by making an asymptotic expansion. MSC 1991: 53C07, 53C25, 81T13, 81C60

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Cite this paper

@inproceedings{Kanno1999OctonionicYI, title={Octonionic Yang-Mills Instanton on Quaternionic Line Bundle of Spin(7) Holonomy}, author={Hiroaki Kanno and Yukinori Yasui}, year={1999} }