Anomalies, Local Counter Terms and Bosonization

TL;DR

This paper re-examines local counter terms in quantum anomalies, highlighting their role in gauge theories and bosonization, and clarifying their proper definition and impact on the Jacobian and kinetic terms.

Contribution

It clarifies the role of local counter terms in quantum anomalies, especially in bosonization, and shows some Jacobian contributions cannot be removed by local counter terms.

Findings

A part of the Jacobian cannot be removed by local counter terms.

Local counter terms depend on the physical context, such as gauge theory or bosonization.

The Jacobian contributes to the kinetic term in bosonization.

Abstract

We re-examine the issue of local counter terms in the analysis of quantum anomalies. We analyze two-dimensional theories and show that the notion of local counter terms need to be carefully defined depending on the physics contents such as whether one is analyzing gauge theory or bosonization. It is shown that a part of the Jacobian, which is apparently spurious and eliminated by a local counter term corresponding to the mass term of the gauge field in gauge theory, cannot be removed by a {\it local} counter term and plays a central role by giving the kinetic term of the bosonized field in the context of path integral bosonization.