Higher-order Lorentz-invariance violation, quantum gravity and fine-tuning

TL;DR

This paper investigates Lorentz invariance violation in higher-order effective theories, focusing on quantum electrodynamics extensions with dimension-five operators, and assesses the fine-tuning and bounds on Lorentz-violating parameters.

Contribution

It analyzes the radiative corrections in Myers-Pospelov QED, demonstrating finite small corrections in the even sector and identifying unsuppressed Lorentz violation effects in the odd sector.

Findings

Small finite radiative corrections in the even sector.

Unsuppressed Lorentz violation effects in the odd sector.

Bound on Lorentz-violating parameter: xi<610^{-3}.

Abstract

The issue of Lorentz fine-tuning in effective theories containing higher-order operators is studied. To this end, we focus on the Myers-Pospelov extension of QED with dimension-five operators in the photon sector and standard fermions. We compute the fermion self-energy at one-loop order considering its even and odd $CPT$ contributions. In the even sector we find small radiative corrections to the usual parameters of QED which also turn to be finite. In the odd sector the axial operator is shown to contain unsuppressed effects of Lorentz violation leading to a possible fine-tuning. We use dimensional regularization to deal with the divergencies and a generic preferred four-vector. Taking the first steps in the renormalization procedure for Lorentz violating theories we arrive to acceptable small corrections allowing to set the bound $\xi<6 \times10^{-3}$.