Arbitrariness in the gravitational Chern-Simons-like term induced radiatively

Abstract

The induction of a Lorentz- and CPT-violating Chern-Simons-like term in a fermionic theory embedded in linearized quantum gravity is reassessed. We explicitly show that gauge symmetry on underlying Feynman diagrams does not fix the arbitrariness inherent to such induced term at one loop order. We present the calculation in a nonperturbative expansion in the Lorentz-violating parameter ${b}_{\ensuremath{\mu}}$ and within a framework which, besides operating in the physical dimension, judiciously parametrizes regularization dependent arbitrary parameters usually fixed by symmetries.