BF gravity with Immirzi parameter and matter fields

TL;DR

This paper develops a polynomial action framework for coupling matter fields and a cosmological constant to BF gravity with an Immirzi parameter, facilitating the understanding of matter-gravity interactions.

Contribution

It introduces auxiliary fields to maintain polynomial dependence and derives first- and second-order actions for matter-coupled BF gravity with the Immirzi parameter.

Findings

Recovered Holst and second-order actions for gravity with matter

Expressed auxiliary fields in terms of physical fields

Enhanced understanding of matter coupling in BF theory

Abstract

We perform the coupling of the scalar, Maxwell, and Yang-Mills fields as well as the cosmological constant to BF gravity with Immirzi parameter. The proposed action principles employ auxiliary fields in order to keep a polynomial dependence on the B fields. By handling the equations of motion for the B field and for the auxiliary fields, these latter can be expressed in terms of the physical fields and by substituting these expressions into the original action principles we recover the first-order (Holst) and second-order actions for gravity coupled to the physical matter fields. We consider these results a relevant step towards the understanding of the coupling of matter fields to gravity in the theoretical framework of BF theory.