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arXiv · hep-th/9612182

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

B. S. Acharya·M. O'Loughlin
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Abstract

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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BibTeXRIS

B. S. Acharya, M. O'Loughlin. 1996-12-23. Self-Duality in D <= 8-dimensional Euclidean Gravity. https://doi.org/10.1103/physrevd.55.r4521

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