Matter matters in Einstein-Cartan gravity

TL;DR

This paper explores how matter fields interact with Einstein-Cartan gravity, showing that nonpropagating torsion leads to contact interactions in an equivalent metric formulation, with potential extensions involving curvature-squared terms.

Contribution

It constructs a broad class of models with nondynamical torsion and derives their equivalent metric theories with specific matter interactions.

Findings

Gravitational spectra include only the massless graviton.

Elimination of non-propagating degrees yields contact interactions.

Inclusion of curvature-squared terms is briefly discussed.

Abstract

We study scalar, fermionic and gauge fields coupled nonminimally to gravity in the Einstein-Cartan formulation. We construct a wide class of models with nondynamical torsion whose gravitational spectra comprise only the massless graviton. Eliminating non-propagating degrees of freedom, we derive an equivalent theory in the metric formulation of gravity. It features contact interactions of a certain form between and among the matter and gauge currents. We also discuss briefly the inclusion of curvature-squared terms.