# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### Oxidation of self-duality to 12 dimensions and beyond

##### MPS-Authors

##### Locator

There are no locators available

##### Fulltext (public)

1212.6270

(Preprint), 219KB

Devchand03_2014.pdf

(Any fulltext), 364KB

##### Supplementary Material (public)

There is no public supplementary material available

##### 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.