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Selfduality in D <= eight-dimensional Euclidean gravity

Research output: Contribution to journalArticle

Bobby Samir Acharya, M. O'Loughlin

Original languageUndefined/Unknown
Pages (from-to)4521-4524
Number of pages4
Publication statusPublished - 15 Apr 1997

King's Authors


In the context of D-dimensional Euclidean gravity, we define the natural generalization to D dimensions of the self-dual Yang-Mills equations as duality conditions on the curvature two-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU(2), SU(3), G2, 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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