Plebanski gravity without the simplicity constraints

Understand

In Plebanski's self-dual formulation general relativity becomes SO(3) BF theory supplemented with the so-called simplicity (or metricity) constraints for the B-field.

• The main dynamical equation of the theory states that the curvature of the B-compatible SO(3) connection is self-dual, with the notion of self-duality being defined by the B-field.
• We describe a theory obtained by dropping the metricity constraints, keeping only the requirement that the curvature of the B-compatible connection is self-dual.
• It turns out that the theory one obtains is to a very large degree fixed by the Bianchi identities.