Reparametrisation invariance, anomalies and pseudoscalar states in massless quantum electrodynamics

Abstract

In electrodynamics, and more generally in gauge theories, quantisation introduces an ambiguity whereby the vector current, the axial current, or both may acquire an anomalous divergence. These anomalies can be classified as relevant, conventionally associated with the infrared properties of the theory, and irrelevant, arising from the freedom in the choice of renormalisation scheme. We show that, under a axial reparametrisation of the fermion fields, the global axial symmetry can be promoted to a gauge redundancy. Requiring this gauge symmetry to be preserved at the quantum level eliminates the irrelevant anomalies, leaving a non-propagating pseudoscalar field that acts as a Lagrange multiplier enforcing the familiar axial anomaly. We further argue that, on topologically non-trivial spacetimes, in particular those with non-trivial second cohomology, this axial gauge symmetry can undergo a Higgs mechanism, rendering the pseudoscalar field an emergent propagating degree of freedom. Finally, we briefly point out an analogous emergent state associated with the conformal anomaly.