Coordinate and Kähler $σ$-Model Anomalies and Their Cancellation in String Effective Field Theories

Abstract

We discuss the complete set of one-loop triangle graphs involving the Yang-Mills gauge connection, the \Kahler\ connection and the $σ$-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 $σ$-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 $σ$-model coordinate symmetry based upon the introduction of two types of counterterms. Finally, we enlarge the $σ$-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.