A note on pure connection formalism for unimodular gravity and its possible generalisations

TL;DR

This paper explores the pure connection formalism for Henneaux-Teitelboim unimodular gravity, deriving a pure connection action and demonstrating its inclusion in a broader class of gauge theories with two degrees of freedom.

Contribution

It derives the pure connection action for Henneaux-Teitelboim unimodular gravity and shows its relation to a wider class of gauge theories with broken diffeomorphism invariance.

Findings

Derived the pure connection action from Plebanski formulation.

Included Henneaux-Teitelboim UG in a broader class of theories.

Propagates two complex degrees of freedom.

Abstract

In this note, we consider the Henneaux-Teitelboim version of Unimodular Gravity (UG) and its deformations in the form of gauge theories with spontaneously broken diffeomorphism invariance. Actions defining such theories depends on the curvature of an $SO(3,\mathbb{C})$ gauge connection and the field strength of a (real) 3-form (or equivalently its dual vector density). We obtain the pure connection action of the theory from the corresponding Plebanski action by integrating out auxiliary fields. Then we show that the Henneaux-Teitelboim form of UG can be included in a wider class of theories which propagate two (complex) degrees of freedom.