Anomalous U(1)s in Type I superstring vacua

TL;DR

This work provides a systematic one-loop string calculation of anomalous U(1) gauge boson masses in four-dimensional orientifolds, revealing that mass terms arise from Green-Schwarz couplings to RR axions and depend on sector localization. N=1 sectors contribute mass terms localized in all six internal dimensions, while N=2 sectors contribute terms localized in four dimensions, allowing U(1) gauge bosons to be lighter than the string scale and potentially mediate submillimeter forces. The analysis includes explicit orientifold examples, showing how internal volumes control the masses and illustrating various brane/bulk axion configurations. The results have direct implications for Standard Model realizations in brane-worlds, global symmetries, and potential experimental signatures, including non-universal forces and collider phenomenology, with caveats on preserving massless hypercharge in certain limits.

Abstract

We perform a systematic string computation of the masses of anomalous U(1) gauge bosons in four-dimensional orientifold vacua, and we study their localization properties in the internal (compactified) space. We find that N=1 supersymmetric sectors yield four-dimensional contributions, localized in the whole six-dimensional internal space, while N=2 sectors give contributions localized in four internal dimensions. As a result, the U(1) gauge fields can be much lighter than the string scale, so that when the latter is at the TeV, they can mediate new non-universal repulsive forces at submillimeter distances much stronger than gravity. We also point out that even U(1)s which are free of four-dimensional anomalies may acquire non-zero masses as a consequence of six-dimensional anomalies.