Self-duality in D{le}8-dimensional Euclidean gravity
- Queen Mary and Westfield College, Mile End Road, London, E1 4NS (United Kingdom)
- ICTP, P.O. Box 586, Trieste, 34014 (Italy)
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), G{sub 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. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 491678
- Journal Information:
- Physical Review, D, Journal Name: Physical Review, D Journal Issue: 8 Vol. 55; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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