Schwinger terms in Weyl-invariant and diffeomorphism-invariant 2-d scalar field theory

TL;DR

This paper calculates Schwinger terms in the energy-momentum tensor algebra for 2D massless scalar fields, showing these terms are unaffected by regularization or background metric, highlighting their fundamental nature.

Contribution

It provides a novel computation of Schwinger terms in 2D scalar field theories, emphasizing their independence from regularization and background geometry.

Findings

Schwinger terms are regularization-independent.

Schwinger terms do not depend on the background metric.

The results clarify the fundamental nature of these anomalies.

Abstract

We compute the Schwinger terms in the energy-momentum tensor commutator algebra from the anomalies present in Weyl-invariant and diffeomorphism-invariant effective actions for two dimensional massless scalar fields in a gravitational background. We find that the Schwinger terms are not sensitive to the regularization procedure and that they are independent of the background metric.