Chiral and scale anomalies of non local Dirac operators

TL;DR

This paper computes the chiral and scale anomalies of a broad class of non-local Dirac operators using zeta-function regularization, demonstrating that non-locality does not alter the standard minimal anomaly form.

Contribution

It introduces a general framework for analyzing anomalies of non-local Dirac operators and shows that their anomalies can be rendered equivalent to local cases through counterterms.

Findings

Non-local Dirac operators have standard minimal anomalies.

Counterterms can remove new terms introduced by non locality.

Anomalies are consistent with known local operator results.

Abstract

The chiral and scale anomalies of a very general class of non local Dirac operators are computed using the $\zeta$-function definition of the fermionic determinant. For the axial anomaly all new terms introduced by the non locality are shown to be removable by counterterms and such counterterms are also explicitly computed. It is verified that the non local Dirac operators have the standard minimal anomaly in Bardeen's form.