Partially-flat gauge fields on manifolds of dimension greater than four

Details Partially-flat gauge fields on manifolds of dimension greater than four Partially-flat gauge fields on manifolds of dimension greater than four

2002-05-03

arxiv.org/abs/hep-th/0205030v2

Physics

High Energy Physics

High Energy Physics - Theory

8 pages

Scientific paper

We describe two extensions of the notion of a self-dual connection in a vector bundle over a manifold M from dim M=4 to higher dimensions. The first extension, Omega-self-duality, is based on the existence of an appropriate 4-form Omega on the Riemannian manifold M and yields solutions of the Yang-Mills equations. The second is the notion of half-flatness, which is defined for manifolds with certain Grassmann structure T^C M \cong E \otimes H. In some cases, for example for hyper-Kaehler manifolds M, half-flatness implies Omega-self-duality. A construction of half-flat connections inspired by the harmonic space approach is described. Locally, any such connection can be obtained from a free prepotential by solving a system of linear first order ODEs.

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