THE GRAVITATIONAL CORRECTION TO PCAC

A simple-minded perturbation calculation to order G (the Newtonian gravitational constant) of the two-graviton coupling to a pseudoscalar (P) or axial (A) current via a fermion loop gives an anomalous contribution which can be added to the Adler term in the form ∂_αA_α = 2m P + e²ε_kλμν F_kλF_μν/16π² + ε_kλμνR_kλρσR_μνρσ/768π². The anomalous terms can be interpreted as arising from an infinite-mass regulating loop.