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

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.