Comment on “Topological invariants, instantons, and the chiral anomaly on spaces with torsion”

Abstract

In Riemann-Cartan spacetimes with torsion only its axial covector piece $A$ couples to massive Dirac fields. Using renormalization group arguments, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d^\star A$, as has been claimed in a recent paper [PRD 55, 7580 (1997)].