Self-Duality in D <= 8-dimensional Euclidean Gravity

Details Self-Duality in D <= 8-dimensional Euclidean Gravity Self-Duality in D <= 8-dimensional Euclidean Gravity

1996-12-17

arxiv.org/abs/hep-th/9612182v2

Phys.Rev.D55:4521-4524,1997

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, Latex, factors in eqn. (6) corrected, acknowledgement and reference added, typos fixed

Scientific paper

10.1103/PhysRevD.55.R4521

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU(2), SU(3), G_2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lower dimensions. By considering gauge fields propagating on these self-dual manifolds and embedding the spin connection in the gauge connection, solutions to the D-dimensional equations for self-dual Yang-Mills fields are found. We show that the Yang-Mills action on such manifolds is topologically bounded from below, with the bound saturated precisely when the Yang-Mills field is self-dual. These results have a natural interpretation in supersymmetric string theory.

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