CDJ formulation from the instanton representation of Plebanski gravity

TL;DR

This paper demonstrates how the CDJ formulation of gravity can be derived from the instanton representation of Plebanski gravity, highlighting symmetry properties in the process.

Contribution

It provides a derivation linking the CDJ formulation to the instanton representation, illustrating symmetry commutation in gravitational actions.

Findings

Derived the CDJ action from the instanton representation

Showed symmetry commutation between basic fields and equations of motion

Clarified the relationship between different gravity formulations

Abstract

We show that a certain action which gives rise to the pure spin connection formulation of gravity by CDJ can be consistently derived from the action for the instanton representation of Plebanski gravity. This is an illustrative example of when certain symmetries of the basic fields commute with the symmetries of the equations of motion.