General Relativity from Three-Forms in Seven Dimensions

Abstract

We consider a certain theory of 3-forms in 7 dimensions, and study its dimensional reduction to 4D, compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius. We show that the resulting 4D theory is General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian. Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of S^3. Realistic values of Lambda correspond to S^3 of Planck size.

5 pages, no figures

References in corpus (5)

• Renormalizable Non-Metric Quantum Gravity?
• Plebanski gravity without the simplicity constraints
• Non-Metric Gravity II: Spherically Symmetric Solution, Missing Mass and Redshifts of Quasars
• 6D Interpretation of 3D Gravity
• Topological field theories of 2- and 3-forms in six dimensions

Cited by in corpus (6)

• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Fermions, differential forms and doubled geometry
• Deformations of GR, Geometrodynamics and Reality Conditions
• Topological field theories of 2- and 3-forms in six dimensions
• Dynamics of 3-Forms in Seven Dimensions
• New Reflections on Gravitational Duality