Plebanski gravity without the simplicity constraints

TL;DR

This paper explores a modified formulation of Plebanski gravity where the usual simplicity constraints are dropped, resulting in a theory that still describes gravity with two degrees of freedom, largely determined by Bianchi identities.

Contribution

It introduces a gravity theory derived from Plebanski's formulation without the simplicity constraints, showing it retains key features of general relativity.

Findings

The resulting theory still describes gravity with two propagating degrees of freedom.

The theory is largely constrained by Bianchi identities despite dropping simplicity constraints.

It provides a new perspective on the foundational structure of gravity theories.

Abstract

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. Moreover, it is still a gravity theory, with just two propagating degrees of freedom as in GR.