Nonuniversal anomalies in heterotic string constructions

Abstract

We investigate anomalies on heterotic orbifolds and their blowups. We give a simple example of an orbifold blowup which contains anomalous $U(1)$ symmetries that are canceled by axions which couple non-universally to the different gauge groups, thus clarifying some confusion which recently arose in the literature concerning anomaly universality. We argue that non-universal axionic couplings are the general case, and that the couplings are only universal in the case of orbifolds. We comment on the consequences of this non-universality for discrete $R$ symmetries. We furthermore investigate the origin of discrete ($R$ and non-$R$) symmetries on smooth Calabi--Yau manifolds.