Effective field theory reproducing the MOND phenomenology based on a non-Abelian Yang-Mills graviphoton

TL;DR

The paper introduces an EFT-based MOND framework in which a fundamental SU(2) Yang-Mills gauge field acts as a gravitophoton that couples to a dipolar dark matter medium. The dark matter dipoles polarize under the gravitational and YM fields, generating a dielectric-like modification of gravity that naturally yields the deep MOND limit, with the MOND scale $a_0$ tied to the EFT parameter $\alpha$ by $a_0 \sim c^2/\alpha$. A covariant extension using the Khronon scalar field restores diffeomorphism invariance in principle, though the fully covariant theory is shown to apply cleanly mainly to stationary systems. While the construction elegantly intertwines MOND phenomenology with a new particle-physics sector, it leaves open the transition to the Newtonian/GR regime and cosmological applications, inviting further development of the microphysical underpinnings and non-stationary extensions.

Abstract

Motivated by the phenomenology of MOND, we propose a theory based on a fundamental non Abelian Yang-Mills gauge field with gravitational coupling constant (a "graviphoton") emerging in a regime of weak acceleration, i.e. below the MOND acceleration scale. Using the formalism of the effective field theory and invoking a mechanism of gravitational polarization of the dark matter medium, we show that generic solutions of this theory reproduce the deep MOND limit without having to introduce in an ad hoc way an arbitrary function in the action. In this framework, MOND is due to the existence of a new sector of the standard model of particle physics. Furthermore, the model involves a violation of the local Lorentz invariance in the low acceleration regime. We show how to restore the general covariance of the model by adding one gravitational degree of freedom in the form of the scalar Khronon field.