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

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.

16 pages

References in corpus (10)

• Signals for Lorentz Violation in Post-Newtonian Gravity
• Matter-gravity couplings and Lorentz violation
• The effects of Chern-Simons gravity on bodies orbiting the Earth
• A gravitational-wave probe of effective quantum gravity
• Gauge Invariance and the Pauli-Villars Regulator in Lorentz- and CPT-Violating Electrodynamics
• Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED
• A new PPN parameter to test Chern-Simons gravity
• Lorentz violation and the proper-time method
• Papapetrou Energy-Momentum Tensor for Chern-Simons Modified Gravity
• On the ambiguities in the effective action in Lorentz-violating gravity

Cited by in corpus (17)

• Backgrounds in gravitational effective field theory
• Partitioning Dense Graphs with Hardware Accelerators
• Effective electromagnetic actions for Lorentz violating theories exhibiting the axial anomaly
• Lorentz invariance violation and the CPT-odd electromagnetic response of a tilted anisotropic Weyl semimetal
• On perturbative aspects of a nonminimal Lorentz-violating QED with CPT-odd dimension-5 terms
• On plane wave solutions in Lorentz-violating extensions of gravity
• Classical radiation fields for scalar, electromagnetic, and gravitational waves with spacetime-symmetry breaking
• Aspects of the Equivalence Between the $f^{\mu }$ and $c^{\nu \mu }$ Terms in Lorentz-Violating Quantum Field Theory
• Axion-Photon Interaction from Nonminimal Dimension-5 Lorentz-Violating Operators
• Bounds on Vacuum-Orthogonal Lorentz and CPT Violation from Radiative Corrections
• The full Lorentz-violating vacuum polarization tensor: low and high energy limits
• Effective electromagnetic Lagrangians in the derivative expansion method
• Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay
• Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay
• Carroll-Field-Jackiw term in a massless Rarita-Schwinger model
• Lorentz Violation and Radiative Corrections in Gauge Theories
• First Order Axial Perturbation of the Reissner-Nordström Metric in a Possible Parity-Violating Gravity Background