I will derive an isomorphism between a Cartan-3-form Weyl-theory in 7-D and general relativity in Plebanski formulation and discuss the depth and impact. Basically, that the 4D Lagrangian:
is an exact description of general relativity, where is given by:
and the metric-volume form implicitly defining , namely, , is:
with the 3-form on a 7-D manifold is explicitly defined by the -holomorphic metric:
with the action:
Such holomorphic 3-forms in 7-D are analytically related to the exceptional group , which can be interpreted as the subgroup of that metaplectically stabilizes generic 3-forms.