Radiative corrections in metric-affine bumblebee model

TL;DR

This paper investigates the metric-affine bumblebee gravity model, deriving its field equations, analyzing the weak-field limit, and showing the coupling of the bumblebee field to matter, with implications for renormalizability and non-metricity.

Contribution

It provides a detailed derivation of the field equations in the metric-affine bumblebee model and explores the phenomenological effects of the bumblebee field coupling to matter.

Findings

Connection expressed as Levi-Civita of a disformally related metric

Effective theory is renormalizable at one-loop level

Non-metricity linked to the gradient of the bumblebee field

Abstract

We consider the metric-affine formulation of bumblebee gravity, derive the field equations, and show that the connection can be written as Levi-Civita of a disformally related metric in which the bumblebee field determines the disformal part. As a consequence, the bumblebee field gets coupled to all the other matter fields present in the theory, potentially leading to nontrivial phenomenological effects. To explore this issue we compute the weak-field limit and study the resulting effective theory. In this scenario, we couple scalar and spinorial matter to the effective metric which, besides the zeroth-order Minkowskian contribution, also has the vector field contributions of the bumblebee, and show that it is renormalizable at one-loop level. From our analysis it also follows that the non-metricity of this theory is determined by the gradient of the bumblebee field, and that it can acquire a vacuum expectation value due to the contribution of the bumblebee field.