4D Anomalous U(1)'s, their masses and their relation to 6D anomalies

TL;DR

This work demonstrates that four-dimensional non-anomalous $U(1)$ gauge bosons can become massive when the theory decompactifies to six dimensions, because six-dimensional mixed anomalies feed into four-dimensional masses through the Green–Schwarz mechanism and UV tadpoles on the annulus. By computing the UV tadpole contributions and performing explicit decompactification analyses in $Z'_6$ and $Z_6$ orientifolds, the authors connect six-dimensional anomaly cancellation to four-dimensional mass patterns across several models ($Z_2$, $Z_3$, $Z_4$, $Z_6$) and their decompactified limits. The results show that the six-dimensional mass terms reproduce volume-dependent parts of the four-dimensional masses, and they identify anomaly-free combinations that remain massless in certain limits, with clear implications for model-building and potential collider signals if the string scale is low. Overall, the paper elucidates a concrete mechanism by which higher-dimensional anomalies influence low-energy $U(1)$ physics in string constructions, guiding the identification of massless hypercharge candidates and the phenomenology of extra gauge bosons.

Abstract

In some four-dimensional orientifolds, U(1) gauge fields that are free of four-dimensional anomalies can still be massive. It is shown that this is due to mass-generating six-dimensional anomalies. Six-dimensional anomalies affect four-dimensional masses via decompactifications.