Anomaly cancellation in effective supergravity theories from the heterotic string: two simple examples

TL;DR

This paper demonstrates how to cancel anomalies in effective supergravity theories derived from heterotic string compactifications using Pauli-Villars regularization and a generalized Green-Schwarz mechanism, aligning with string calculations.

Contribution

It shows that anomaly coefficients depend only on a single holomorphic function of moduli, enabling universal cancellation in specific heterotic models.

Findings

Anomaly coefficients depend on a single holomorphic function.

Anomaly cancellation achieved via a generalized Green-Schwarz mechanism.

Results match string theory calculations for Z3 and Z7 models.

Abstract

We use Pauli-Villars regularization to evaluate the conformal and chiral anomalies in the effective field theories from Z3 and Z7 compactifications of the heterotic string without Wilson lines. We show that parameters for Pauli-Villars chiral multiplets can be chosen in such a way that the anomaly is universal in the sense that its coefficient depends only on a single holomorphic function of the three diagonal moduli. It is therefore possible to cancel the anomaly by a generalization of the four-dimensional Green-Schwarz mechanism. In particular we are able to reproduce the results of a string calculation of the four-dimensional chiral anomaly for these two models.