There is no ambiguity in the radiatively induced gravitational Chern-Simons term

Brett Altschul

doi:10.1103/physrevd.99.125009

Abstract

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. Lorentz symmetry in a metric theory of gravity can only be broken spontaneously, and when the vector $b^{\mu}$ arises from spontaneous symmetry breaking, these specific radiative corrections are no longer ambiguous but instead must vanish identically.

Highlights

Since the 1990s, there had been a significant renewal of interest in the possibility that the seemingly absolute Lorentz and CPT symmetries of the standard model and gravity might be very weakly violated
Even if there is no current evidence for Lorentz or CPT violation, these symmetries are so basic that they are worthy of careful study
The general effective field theory (EFT) describing Lorentz violation in particle physics includes the most general CPT violation as well. This EFT is known as the standard model extension (SME) [2,3]

Summary

INTRODUCTION

Since the 1990s, there had been a significant renewal of interest in the possibility that the seemingly absolute Lorentz and CPT symmetries of the standard model and gravity might be very weakly violated. At this time, there is no compelling evidence for such symmetry breaking. The general EFT describing Lorentz violation in particle physics includes the most general CPT violation as well This EFT is known as the standard model extension (SME) [2,3]. The usual standard model action is formed by writing down all the local, renormalizable, SUð3Þc × SUð2ÞL × Uð1ÞY gauge-invariant, Lorentz-invariant operators that can be constructed from those fields. This paper will both introduce this puzzle and proceed to solve it

THE PUZZLE OF GRAVITATIONAL RADIATIVE CORRECTIONS

STRUCTURE OF AMBIGUOUS CORRECTIONS

Abelian theory

Gravitational theory

RESOLVING THE PUZZLE