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.

arXiv comment96 pages

References in corpus (34)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• f(T) teleparallel gravity and cosmology
• Coincident General Relativity
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• The covariant formulation of f(T) gravity
• Agravity
• Nonmetricity formulation of general relativity and its scalar-tensor extension
• The Higgs Phenomenon in Quantum Gravity
• Unitarity, stability and loops of unstable ghosts
• Ghosts in metric-affine higher order curvature gravity
• General Teleparallel Quadratic Gravity
• Solution to the ghost problem in fourth order derivative theories
• The Electroweak Chiral Lagrangian for the Standard Model with a Heavy Higgs
• The spectrum of symmetric teleparallel gravity
• A New Class of Ghost and Tachyon Free Metric Affine Gravities
• Quantum Gravity, Fakeons And Microcausality
• Instabilities in Metric-Affine Theories of Gravity
• The Ultraviolet Behavior Of Quantum Gravity
• A Higgs Mechanism for Gravity
• Scale transformations in metric-affine geometry
• The Higgs sector of gravitational gauge theories
• Tree-Level Unitarity Constraints on the Gravitational Couplings of Higher-Spin Massive Fields
• The role of nonmetricity in metric-affine theories of gravity
• Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?
• On quantum corrections in higher-spin theory in flat space
• High energy bosons do not propagate
• Radiatively stable ghost and tachyon freedom in Metric Affine Gravity
• Linear connections with propagating spin-3 field in gravity
• Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories
• Photon-photon scattering from a UV-complete gravity QFT
• Quantum field theories of arbitrary-spin massive multiplets and Palatini quantum gravity
• Massive Higher-Spin Multiplets and Asymptotic Freedom in Quantum Gravity
• Unitarity of Singh-Hagen model in $D$ dimensions
• Mass Generating Antisymmetric Tensor Field Theories

Cited by in corpus (37)

• Inflation in Metric-Affine Quadratic Gravity
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Independent connection in ACTion during inflation
• Inflating and Reheating the Universe with an Independent Affine Connection
• Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• New black hole solutions with a dynamical traceless nonmetricity tensor in Metric-Affine Gravity
• Einstein-Cartan pseudoscalaron inflation
• Teleparallel gravity
• General Effective Field Theory of Teleparallel Gravity
• Inflation in Weyl-invariant Einstein-Cartan gravity
• The origin of Weyl gauging in metric-affine theories
• Dynamical system analysis of Dirac-Born-Infeld scalar field cosmology in coincident $f(Q)$ gravity
• Einstein-Proca theory from the Einstein-Cartan formulation
• Projective transformations in metric-affine and Weylian geometries
• Gibbons-Hawking-York boundary terms and the generalized geometrical trinity of gravity
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Spatially covariant gravity with nonmetricity
• Some simple theories of gravity with propagating torsion
• Constraining Palatini gravity with GR-independent equations of state for neutron stars
• Conformally covariant operators of mixed-symmetry tensors and MAGs
• Stability of Poincaré gauge theory with cubic order invariants
• Covariant spin-parity decomposition of the Torsion and Path Integrals
• Cosmology of Metric-Affine $R+\beta R^2$ Gravity with Pure Shear Hypermomentum
• Some simple theories of gravity with propagating nonmetricity
• Stability in Cubic Metric-Affine Gravity
• Inflation in non-local hybrid metric-Palatini gravity
• Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme
• Friedmann cosmology with hyperfluids
• Radiative corrections to the $R$ and $R^2$ invariants from torsion fluctuations on maximally symmetric spaces
• Thermal Production of Massless Dark Photons
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Alleviating the Hubble tension with Torsion Condensation (TorC)
• Toward a gravitational network: Bridging metric-affine gravity and no-scale supergravity
• Fate of chiral symmetry in Riemann-Cartan geometry
• (In)equivalence of Metric-Affine and Metric Effective Field Theories
• Gravitational waves in Cubic Metric-Affine Gravity