Selfduality in D <= eight-dimensional Euclidean gravity
Dec, 19968 pages
Published in:
- Phys.Rev.D 55 (1997) R4521-R4524
e-Print:
- hep-th/9612182 [hep-th]
Report number:
- QMW-PH-96-28,
- IC-96-264,
- IC-96-276
Citations per year
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.Note:
- 9 pages, Latex, factors in eqn. (6) corrected, acknowledgement and reference added, typos fixed
- 11.25.Mj
- 04.50.+h
- gravitation
- dimension: <=8
- field theory: Euclidean
- duality
- field equations: Yang-Mills
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