String Dualities in the Presence of Anomalous U(1) Symmetries

TL;DR

The paper investigates anomalous $U(1)$ symmetries in $D=4$, $N=1$ string theories, contrasting their realization in heterotic strings with open-string orientifolds. It shows that in type IIB orientifolds the Green–Schwarz mechanism involves twisted moduli and that Fayet–Iliopoulos terms are moduli rather than fixed scales, while anomalous gauge-boson masses remain at the string/Planck scale and largely decouple from FI terms. The authors analyze several explicit heterotic–orientifold pairs to test heterotic–Type I duality, finding that duality holds in some cases (e.g., certain $Z_3$ models) but fails in others (notably $Z_7$ and $Z_3 imes Z_3$), raising questions about the universality of the duality and the role of nonperturbative effects. They also discuss the emergence of global anomalous $U(1)$ symmetries after gauged U(1) decoupling and outline possible phenomenological implications, such as the limited predictive power of FI terms in orientifolds. The work emphasizes that duality is a nuanced, model-dependent property in four dimensions and may require nonperturbative dynamics to be fully realized.

Abstract

Anomalous U(1) gauge symmetries in type II orientifold theories show some unexpected properties. In contrast to the heterotic case, the masses of the gauge bosons are in general of order of the string scale even in the absence of large Fayet-Iliopoulos terms. Despite this fact, the notion of heterotic-type II orientifold duality remains a useful concept, although this symmetry does not seem to hold in all cases considered. We analyse the status of this duality symmetry, clarify the properties of anomalous U(1) gauge symmetry in the orientifold picture and comment on the consequences for phenomenological applications of such anomalous gauge symmetries.