Curved-space trace, chiral, and Einstein anomalies from path integrals, using flat-space plane waves.

Abstract

We show that the gravitational trace and chiral anomalies can be computed from the measure by using the same general flat-space methods as used for nongravitational anomalies. No heat-kernel methods, zeta-function regularization, point-splitting techniques, etc., are needed, although they may be used and then simplify the algebra. In particular, we claim that it is not necessary to insert factors of ${g}^{1/4}$ which are often added on grounds of covariance, since one-loop anomalies are local objects, while the trace of the Jacobian of the measure is a purely mathematical object which can be evaluated whether or not one has even heard about general relativity. We also show that the trace operation is cyclic by performing two different computations of the Einstein anomaly: once with the regulator in front of the Jacobian and once in the back. In both cases we obtain total derivatives on a plane-wave basis.