Coordinate and K\"{a}hler $\sigma$-Model Anomalies and Their Cancellation in String Effective Field Theories

TL;DR

This paper analyzes one-loop anomalies in string effective field theories of orbifolds, focusing on gauge, Kähler, and sigma-model coordinate anomalies, and proposes mechanisms for their cancellation.

Contribution

It introduces a comprehensive analysis of anomalies in orbifold models and proposes new counterterm-based mechanisms for their cancellation, extending the Green-Schwarz approach.

Findings

Identified complete set of one-loop anomalies in orbifold models.

Proposed counterterm mechanisms for anomaly cancellation.

Extended Green-Schwarz mechanism to broader anomaly classes.

Abstract

We discuss the complete set of one-loop triangle graphs involving the Yang-Mills gauge connection, the \Kahler\ connection and the $\sigma$-model coordinate connection in the effective field theory of $(2,2)$ symmetric $Z_N$ orbifolds. That is, we discuss pure gauge, pure \Kahler\ and pure $\sigma$-model coordinate anomalies as well as the mixed anomalies, such as \Kahler-gauge, some of which have been discussed elsewhere. We propose a mechanism for restoring both \Kahler\ and $\sigma$-model coordinate symmetry based upon the introduction of two types of counterterms. Finally, we enlarge the $\sigma$-model generalization of the Green-Schwarz mechanism to allow the removal of the universal parts of a wider class of anomalies than those previously discussed.