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Journal Article

Oxidation of self-duality to 12 dimensions and beyond

MPS-Authors

Devchand,  Chandrashekar
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1212.6270
(Preprint), 219KB

Devchand03_2014.pdf
(Any fulltext), 364KB

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Citation

Devchand, C. (2014). Oxidation of self-duality to 12 dimensions and beyond. Communications in Mathematical Physics, 329(2), 461-482. doi:10.1007/s00220-014-1996-y.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-74CF-A
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 K\"ahler 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.