Effective fermion kinematics from a modified quantum gravity

TL;DR

This paper derives the effective dispersion relations for fermions and scalars in two different quantum gravity models, revealing similar IR phenomenology and constraints on Lorentz violation despite their UV differences.

Contribution

It provides a comparative analysis of matter kinematics in Einstein and Horava-Lifshitz gravity models, highlighting IR similarities and fine-tuning possibilities.

Findings

Both models suggest a characteristic scale of 10^{10} GeV for Lorentz violation constraints.

Fine-tuning of parameters can cancel Lorentz violation indicators in both models.

IR phenomenology is similar despite UV divergence differences.

Abstract

We consider a classical fermion and a classical scalar, propagating on two different kinds of 4-dimensional diffeomorphism breaking gravity backgrounds, and we derive the one-loop effective dispersion relation for matter, after integrating out gravitons. One gravity model involves quadratic divergences at one-loop, as in Einstein gravity, and the other model is the $z=3$ non-projectable Horava-Lifshitz gravity, which involves logarithmic divergences only. Although these two models behave differently in the UV, the IR phenomenology for matter fields is comparable: {\it(i)} for generic values for the parameters, both models identify $10^{10}$ GeV as the typical characteristic scale above which they are not consistent with current upper bounds on Lorentz symmetry violation; {\it(ii)} on the other hand there is always, for both models, a fine-tuning of parameters which allows the cancellation of the indicator for Lorentz symmetry violation.