Localized anomalies in heterotic orbifolds

TL;DR

This paper investigates localized anomalies in heterotic orbifolds, demonstrating local cancellation of non-Abelian anomalies at fixed points and analyzing the structure of anomalous U(1)s in Z_3 models.

Contribution

It provides a detailed analysis of localized anomalies in heterotic Z_3 orbifolds, showing local non-Abelian anomaly cancellation and exploring the structure of anomalous U(1)s.

Findings

Non-Abelian anomalies cancel locally at fixed points.

Anomalous U(1)s can be present at fixed points, but only one per point.

Constructing a single generator for all anomalous U(1)s is generally not possible.

Abstract

Recently spatially localized anomalies have been considered in higher dimensional field theories. The question of the quantum consistency and stability of these theories needs further discussion. Here we would like to investigate what string theory might teach us about theories with localized anomalies. We consider the Z_3 orbifold of the heterotic E_8 x E_8 theory, and compute the anomaly of the gaugino in the presence of Wilson lines. We find an anomaly localized at the fixed points, which depends crucially on the local untwisted spectra at those points. We show that non-Abelian anomalies cancel locally at the fixed points for all Z_3 models with or without additional Wilson lines. At various fixed points different anomalous U(1)s may be present, but at most one at a given fixed point. It is in general not possible to construct one generator which is the sole source of the anomalous U(1)s at the various fixed points.