Topological Gravity versus Supergravity on Manifolds with Special Holonomy

Abstract

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.

LateX file, 19 pages

Cited by in corpus (9)

• Einsteinian gravity from a topological action
• Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds
• Eight-Dimensional Topological Gravity and its Correspondence with Supergravity
• Self-Dual Supergravity in Seven Dimensions with Reduced Holonomy G_2
• The topological structure of supergravity: an application to supersymmetric localization
• Supergravity and the Knitting of the Kalb--Ramond Two-Form in Eight-Dimensional Topological Gravity
• Four-dimensional topological Einstein-Maxwell gravity
• Symmetries and observables in topological gravity
• Gravitational Topological Quantum Field Theory Versus N = 2 D = 8 Supergravity and its lift to N = 1 D = 11 Supergravity