(In)equivalence of Metric-Affine and Metric Effective Field Theories

Abstract

In a geometrical approach to gravity the metric and the (gravitational) connection can be independent and one deals with metric-affine theories. We construct the most general action of metric-affine effective field theories, including a generic matter sector, where the connection does not carry additional dynamical fields. Among other things, this helps in identifying the complement set of effective field theories where there are other dynamical fields, which can have an interesting phenomenology. Within the latter set, we study in detail a vast class where the Holst invariant (the contraction of the curvature with the Levi-Civita antisymmetric tensor) is a dynamical pseudoscalar. In the Einstein-Cartan case (where the connection is metric compatible and fermions can be introduced) we also comment on the possible phenomenological role of dynamical dark photons from torsion and compute interactions of the above-mentioned pseudoscalar with a generic matter sector and the metric. Finally, we show that in an arbitrary realistic metric-affine theory featuring a generic matter sector the equivalence principle always emerges at low energies without the need to postulate it.

v3: matches published version, 31 pages, 1 figure

References in corpus (14)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• Introduction to Effective Field Theory
• Universal Limits on Massless High-Spin Particles
• Metric-Affine Gravity as an Effective Field Theory
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Auxiliary fields representation for modified gravity models
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Torsion Phenomenology at the LHC
• Matter matters in Einstein-Cartan gravity
• Different types of torsion and their effect on the dynamics of fields