General Relativity from Three-Forms in Seven Dimensions

TL;DR

This paper demonstrates that a specific 7D 3-form theory, when dimensionally reduced on a 3-sphere, yields 4D General Relativity with a cosmological constant linked to the sphere's size, connecting higher-dimensional forms to gravity.

Contribution

It shows that 7D 3-form theories can produce 4D GR with a cosmological constant through dimensional reduction, providing a novel geometric origin for the cosmological constant.

Findings

The 4D theory matches GR in Plebanski formulation.

The cosmological constant is proportional to the size of the 3-sphere.

Realistic Lambda values imply Planck-scale 3-sphere size.

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.