Axion anomalies
  We study fermions derivatively coupled to axion-like or pseudoscalar fields,
and show that the axial vector current of the fermions is not conserved in the
limit where the fermion is massless. This violation of the classical chiral
symmetry is due to the background axion field. We compute the contributions to
this anomalous Ward identity due to the pseudoscalar field alone, which arise
in Minkowski space, as well as the effects due to interaction with an external
gravitational field. In all cases, these interactions induce terms in the axion
effective action that can be removed by the addition of local counterterms. We
perform our computations both perturbatively using Feynman graphs, as well as
by studying the transformation properties of the path integral measure. Using
the heat kernel method, we include the effects of gravity as well as gauge
fields, and compute the anomaly. Finally, we verify our relation by considering
derivatively coupled fermions during pseudoscalar-driven inflation and
computing the divergence of the axial current in de Sitter spacetime.
