Consistent matter couplings for Plebanski gravity

TL;DR

This paper introduces a consistent way to couple matter fields to Plebanski gravity, demonstrating equivalence to Einstein--Cartan gravity and supporting various quantization methods.

Contribution

It develops a minimal coupling scheme for matter in Plebanski gravity and proves its consistency through equivalence with Einstein--Cartan gravity.

Findings

Established a covariant matter coupling scheme for Plebanski gravity.

Proved the equivalence of Plebanski plus matter to Einstein--Cartan gravity.

Validated previous matter action proposals within this framework.

Abstract

We develop a scheme for the minimal coupling of all standard types of tensor and spinor field matter to Plebanski gravity. This theory is a geometric reformulation of vacuum general relativity in terms of two-form frames and connection one-forms, and provides a covariant basis for various quantization approaches. Using the spinor formalism we prove the consistency of the newly proposed matter coupling by demonstrating the full equivalence of Plebanski gravity plus matter to Einstein--Cartan gravity. As a byproduct we also show the consistency of some previous suggestions for matter actions.