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arXiv · hep-th/9612230

The Geometry of Self-Dual Gauge Fields

A. H. Bilge·T. Dereli·Ş. Koçak
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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.

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A. H. Bilge, T. Dereli, Ş. Koçak. 1996-12-24. The Geometry of Self-Dual Gauge Fields. https://arxiv.org/abs/hep-th/9612230

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