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 S^4 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.
Keywords
Cite
@article{arxiv.hep-th/9910003,
title = {Octonionic Yang-Mills Instanton on Quaternionic Line Bundle of Spin(7) Holonomy},
author = {H. Kanno and Y. Yasui},
journal= {arXiv preprint arXiv:hep-th/9910003},
year = {2009}
}
Comments
A reference added; 22 pages,a final version to appear J.Geom.Phys