Metric-Affine Gravity as an Effective Field Theory

TL;DR

This paper analyzes metric-affine gravity theories within an effective field theory framework, classifying terms, exploring subclasses, and identifying models with specific particle content and propagating degrees of freedom.

Contribution

It provides a systematic classification of metric-affine gravity theories up to dimension four and explores their particle content and dynamical properties.

Findings

Teleparallel theories can be dynamically equivalent to metric theories.

Certain MAGs have no propagating degrees of freedom.

Constructed MAGs with only a massless graviton and specific spin/parity states.

Abstract

We discuss theories of gravity with independent metric (or frame field) and connection, from the point of view of effective field theory. We count the parity-even Lagrangian terms of dimension up to four and give explicit bases for the independent terms that contribute to the two-point function. We then give the decomposition of the linearized action on a complete basis of spin projectors and consider various subclasses of Metric-Affine Gravity theories (MAGs). We show that teleparallel theories can be dynamically equivalent to any metric theory of gravity and give the particle content of those whose Lagrangian contains only dimension-two terms. We point out the existence of a class of MAGs whose EOMs do not admit propagating degrees of freedoms. Finally, we construct simple MAGs that contain only a massless graviton and a state of spin/parity $2^-$ or $3^-$. As a side result, we write the relativistic wave equation for a spin/parity $2^-$ state.