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arXiv · 1212.6270

Oxidation of self-duality to 12 dimensions and beyond

Chandrashekar Devchand
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Abstract

Using (partial) curvature flows and the transitive action of subgroups of O(d,Z) on the indices {1,...,d} of the components of the Yang-Mills curvature in an orthonormal basis, we obtain a nested system of equations in successively higher dimensions d, each implying the Yang-Mills equations on d-dimensional Riemannian manifolds possessing special geometric structures. This `matryoshka' of self-duality equations contains the familiar self-duality equations on Riemannian 4-folds as well as their generalisations on complex Kähler 3-folds and on 7- and 8-dimensional manifolds with G_2 and Spin(7) holonomy. The matryoshka allows enlargement (`oxidation') to a remarkable system in 12 dimensions invariant under Sp(3). There are hints that the underlying geometry is related to the sextonions, a six-dimensional algebra between the quaternions and octonions.

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Chandrashekar Devchand. 2013-12-25. Oxidation of self-duality to 12 dimensions and beyond. https://doi.org/10.1007/s00220-014-1996-y

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