On the One Loop Fayet-Iliopoulos Term in Chiral Four Dimensional Type I Orbifolds

TL;DR

This paper demonstrates that one loop Fayet-Iliopoulos terms do not arise in certain N=1 open string orbifolds due to topological cancellations, linking this to tadpole cancellation conditions.

Contribution

It shows the absence of one loop Fayet-Iliopoulos terms in specific string models, clarifying the role of worldsheet topology and tadpole cancellation.

Findings

No one loop Fayet-Iliopoulos term is generated in the studied models.

Cancellation occurs between contributions of worldsheets with different topology.

The result is connected to the cancellation of twisted Ramond-Ramond tadpoles.

Abstract

We consider the generation of Fayet-Iliopoulos terms at one string loop in some recently found N=1 open string orbifolds with anomalous U(1) factors with nonvanishing trace of the charge. Low-energy field theory arguments lead one to expect a one loop quadratically divergent Fayet-Iliopoulos term. We show that a one loop Fayet-Iliopoulos term is not generated, due to a cancellation between contributions of worldsheets of different topology. The vanishing of the one loop Fayet-Iliopoulos term in open string compactifications is related to the cancellation of twisted Ramond-Ramond tadpoles.