Metric-Affine Gravity as an effective field theory

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 (MAG) theories. 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 equations of motion 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. (C)& nbsp;2022 Elsevier Inc. All rights reserved.

Automated summary

We discuss theories of gravity with independent metric and connection from the perspective of effective field theory. The parity-even Lagrangian terms up to dimension four are considered, and the decomposition of the linearized action on a complete basis of spin projectors is provided. Various subclasses of Metric-Affine Gravity (MAG) theories are explored, and the existence of MAGs whose equations of motion do not have propagating degrees of freedom is pointed out. Furthermore, simple MAGs containing only a massless graviton and states of spin/parity 2(-) or 3(-) are constructed.