Anomalous U(1)s masses in non-supersymmetric open string vacua

TL;DR

This work extends the string-theoretic calculation of anomalous U(1) masses from supersymmetric to non-supersymmetric open-string vacua using the background-field method. By turning on a magnetic field on D-brane stacks and analyzing the quadratic term in the field, the authors derive UV mass formulas that depend on traces over Chan-Paton matrices and orbifold data, and show that tadpole cancellation reproduces the supersymmetric results while non-vanishing NSNS tadpoles introduce extra contributions. The authors apply the framework to a non-supersymmetric $\mathbb{Z}_2$ orientifold with Scherk-Schwarz breaking, finding explicit masses and noting that the spectrum can remain free of 4D anomalous U(1)s in this setup, though higher-dimensional anomalies can reappear under decompactification. Practically, the results constrain model-building by identifying when a hypercharge-like U(1) can stay massless and by suggesting potential collider signatures for anomalous U(1)s if the string scale is near the TeV range; they also discuss the distinct Higgs-sector contributions to U(1) masses in effective field theory.

Abstract

Anomalous U(1)s are omnipresent in realizations of the Standard Model using D-branes. Such models are typically non-supersymmetric, and the anomalous U(1) masses are potentially relevant for experiment. In this paper, the string calculation of anomalous U(1) masses (hep-th/0204153) is extended to non-supersymmetric orientifolds.