Relaxing Lorentz invariance in general perturbative anomalies

Abstract

We analyze the role of Lorentz symmetry in the perturbative non-gravitational anomalies for a single family of fermions. The theory is assumed to be translational invariant, power-counting renormalizable and based on a local action, but is allowed to have general Lorentz violating operators. We study the conservation of global and gauge currents associate with general internal symmetry groups and find, by using a perturbative approach, that Lorentz symmetry does not participate in the clash of symmetries that leads to the anomalies. We first analyze the triangle graphs and prove that there are regulators for which the anomalous part of the Ward identities exactly reproduces the Lorentz invariant case. Then we show, by means of a regulator independent argument, that the anomaly cancellation conditions derived in Lorentz invariant theories remain necessary ingredients for anomaly freedom.

18 pages, 1 figure. Few comments added. Article published in Physical Review D

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• Effective electromagnetic Lagrangians in the derivative expansion method
• Adler-Bell-Jackiw anomaly in VSR electrodynamics
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• Lorentz-violating extension of Wigner function formalism and chiral kinetic theory
• The Axial Anomaly in Lorentz Violating Theories: Towards the Electromagnetic Response of Weakly Tilted Weyl Semimetals
• CPT, Lorentz invariance and anomalous clash of symmetries