The Geometry of Self-Dual Gauge Fields

Details The Geometry of Self-Dual Gauge Fields The Geometry of Self-Dual Gauge Fields

1996-12-24

arxiv.org/abs/hep-th/9612230v1

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, Latex (No figures) Paper presented to The 9th Max Born Symposium, Karpacz, Poland 25-27 September 1996

Scientific paper

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.

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