Consistent matter couplings for Plebanski gravity

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.