The Geometry of Self-Dual Gauge Fields
Abstract
Self-dual 2-forms in D=2n dimensions are characterised by an eigenvalue criterion. The equivalence of various definitions of self-duality is proven. We show that the self-dual 2-forms determine a n^2-n+1 dimensional manifold S_{2n} and the dimension of the maximal linear subspaces of S_{2n}$ is equal to the Radon-Hurwitz number of linearly independent vector fields on the sphere S^{2n-1}. The relation between the maximal linear subspaces and the representations of Clifford algebras is noted. A general procedure based on this relation for the explicit construction of linearly self-dual 2-forms is given. The construction of the octonionic instanton solution in D=8 dimensions is discussed.
Keywords
Cite
@article{arxiv.hep-th/9612230,
title = {The Geometry of Self-Dual Gauge Fields},
author = {A. H. Bilge and T. Dereli and Ş. Koçak},
journal= {arXiv preprint arXiv:hep-th/9612230},
year = {2007}
}
Comments
14 pages, Latex (No figures) Paper presented to The 9th Max Born Symposium, Karpacz, Poland 25-27 September 1996