Sigma-model anomalies in compact type IIB orientifolds and Fayet-Iliopoulos terms

TL;DR

This paper investigates anomalies in U(1) sigma model symmetries in compact Type IIB orientifolds and demonstrates how a generalized Green-Schwarz mechanism cancels these anomalies, affecting Fayet-Iliopoulos terms.

Contribution

It introduces a generalized Green-Schwarz mechanism involving twisted RR-fields and moduli mixing to cancel anomalies in $Z_N$ orientifolds.

Findings

Anomalies are canceled via twisted RR-field exchange.

Fayet-Iliopoulos terms gain an untwisted modulus dependent component.

The mechanism requires mixing between twisted and untwisted moduli.

Abstract

Compact Type IIB D=4, N=1 orientifolds have certain U(1) sigma model symmetries at the level of the effective Lagrangian. These symmetries are generically anomalous. We study the particular case of $Z_N$ orientifolds and find that these anomalies may be cancelled by a generalized Green-Schwarz mechanism. This mechanism works by the exchange of twisted RR-fields associated to the orbifold singularities and it requires the mixing between twisted and untwisted moduli of the orbifold. As a consequence, the Fayet-Iliopoulos terms which are present for the gauged anomalous U(1)'s of the models get an additional untwisted modulus dependent piece at the tree level.