Topological Gravity versus Supergravity on Manifolds with Special Holonomy

Details Topological Gravity versus Supergravity on Manifolds with Special Holonomy Topological Gravity versus Supergravity on Manifolds with Special Holonomy

2002-01-15

arxiv.org/abs/hep-th/0201109v1

JHEP 0203 (2002) 015

Physics

High Energy Physics

High Energy Physics - Theory

LateX file, 19 pages

Scientific paper

10.1088/1126-6708/2002/03/015

We construct a topological theory for euclidean gravity in four dimensions, by enforcing self-duality conditions on the spin connection. The corresponding topological symmetry is associated to the SU(2) X diffeomorphism X U(1) invariance. The action of this theory is that of d=4, N=2 supergravity, up to a twist. The topological field theory is SU(2) invariant, but the full SO(4) invariance is recovered after untwist. This suggest that the topological gravity is relevant for manifolds with special holonomy. The situation is comparable to that of the topological Yang-Mills theory in eight dimensions, for which the SO(8) invariance is broken down to Spin(7), but is recovered after untwisting the topological theory.

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