There is No Ambiguity in the Radiatively Induced Gravitational Chern-Simons Term

Understand

Quantum corrections to Lorentz- and CPT-violating QED in flat spacetime produce unusual radiative corrections, which can be finite but of undetermined magnitude.

• The corresponding radiative corrections in a gravitational theory are even stranger, since the term in the fermion action involving a preferred axial vector $b^{\mu}$ would give rise to a gravitational Chern-Simons term that is proportional $b^{\mu}$, yet which actually does not break Lorentz invariance.
• Initially, the coefficient of this gravitational Chern-Simons term appears to have the same ambiguity as the coefficient for the analogous term in QED.
• However, this puzzle is resolved by the fact that the gravitational theory has more stringent gauge invariance requirements.