Dynamical Lorentz Symmetry Breaking in a Scale-free Theory of Gravity

TL;DR

This paper investigates how quantum corrections in a scale-free quadratic gravity model with a bumblebee field can lead to spontaneous Lorentz symmetry breaking and generate the Einstein-Hilbert action, linking quantum effects to gravity and Lorentz violation.

Contribution

It demonstrates the dynamical breaking of Lorentz symmetry through radiative corrections in a scale-free gravity model with a bumblebee field, and shows the emergence of Einstein-Hilbert term via quantum effects.

Findings

Bumblebee field acquires a non-trivial VEV through the Coleman-Weinberg mechanism.

Lorentz symmetry is spontaneously broken due to the non-zero VEV of the bumblebee field.

Radiative corrections induce the Einstein-Hilbert term, connecting Planck scale physics to Lorentz violation.

Abstract

This paper explores the renormalization of scale-free quadratic gravity coupled to the bumblebee field and its potential for dynamically breaking Lorentz symmetry. We conduct one-loop renormalization of the model and calculate the associated renormalization group functions. Furthermore, we compute the one-loop effective potential for the bumblebee field, demonstrating that it acquires a non-trivial vacuum expectation value (VEV) through radiative corrections -- a phenomenon known as the Coleman-Weinberg mechanism. This spontaneous breaking of scale invariance, driven by the non-zero VEV of the bumblebee field, leads to Lorentz symmetry violation. As a result, the non-minimal coupling between the bumblebee and gravitational fields induces a spontaneous generation of an Einstein-Hilbert term via radiative corrections, suggesting a possible link between the Planck scale and Lorentz violation phenomena.