Selfduality in D <= eight-dimensional Euclidean gravity

Dec, 1996
8 pages
Published in:
  • Phys.Rev.D 55 (1997) R4521-R4524
e-Print:
Report number:
  • QMW-PH-96-28,
  • IC-96-264,
  • IC-96-276

Citations per year

1997200420112018202401234567
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