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  Oxidation of self-duality to 12 dimensions and beyond

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-74CF-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-001A-0D64-F
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1212.6270 (Preprint), 219KB
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 Creators:
Devchand, Chandrashekar1, Author
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1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              

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Free keywords: High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,
 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.

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 Dates: 2012-12-26201320142014
 Publication Status: Published in print
 Pages: 27 pages
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 Rev. Method: -
 Identifiers: arXiv: 1212.6270
DOI: 10.1007/s00220-014-1996-y
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Title: Communications in Mathematical Physics
Source Genre: Journal
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Pages: - Volume / Issue: 329 (2) Sequence Number: - Start / End Page: 461 - 482 Identifier: -