Spontaneous Lorentz symmetry breaking and one-loop effective action in the metric-affine bumblebee gravity

TL;DR

This paper investigates spontaneous Lorentz symmetry breaking in a metric-affine bumblebee gravity model with fermions, deriving the effective action and potential, and analyzing Lorentz violation effects at one-loop order.

Contribution

It introduces a novel Einstein frame representation with non-minimal fermion couplings and provides an exact fermionic determinant including all non-minimal coupling orders.

Findings

Exact fermionic determinant including all orders in coupling 

Axial contributions are at least second order in  expansion

Computed one-loop effective potential in weak field approximation

Abstract

The metric-affine bumblebee model in the presence of fermionic matter minimally coupled to the connection is studied. We show that the model admits an Einstein frame representation in which the matter sector is described by a non-minimal Dirac action without any analogy in the literature. Such non-minimal terms involve unconventional couplings between the bumblebee and the fermion field. We then rewrite the quadratic fermion action in the Einstein frame in the basis of 16 Dirac matrices in order to identify the coefficients for Lorentz/CPT violation in all orders of the non-minimal coupling $\xi$. The exact result for the fermionic determinant in the Einstein frame, including all orders in $\xi$, is also provided. We demonstrate that the axial contributions are at least of second order in the perturbative expansion of $\xi$. Furthermore, we compute the one-loop effective potential within the weak field approximation.