Metric-Affine Gravity as an Effective Field Theory

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.

96 pages

References in corpus (5)

• The Higgs Phenomenon in Quantum Gravity
• Solution to the ghost problem in fourth order derivative theories
• Linear connections with propagating spin-3 field in gravity
• Quantum field theories of arbitrary-spin massive multiplets and Palatini quantum gravity
• Mass Generating Antisymmetric Tensor Field Theories

Cited by in corpus (2)

• Inflating and Reheating the Universe with an Independent Affine Connection
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity