Anomaly cancellation in D=4, N=1 orientifolds and linear/chiral multiplet duality

TL;DR

The paper addresses gauge and Kahler anomaly cancellation in D=4, N=1 Type IIB orientifolds using a generalized Green-Schwarz mechanism and unveils a duality between linear and chiral multiplets to make the mechanism transparent. It shows that twisted RR 2-forms from the twisted sectors organize into N=1 linear multiplets (except for order-two twists) and that anomaly cancellation reduces to the condition $${\cal A}^{(a)}/(32\pi^2)=\sum_k b_2^{(k,a)} b_3^{(k)}$$ with $b_2^{(k,a)}$ and $b_3^{(k)}$ fixed by the twists (e.g., $b_2^{(k,a)}=c_2 C_k \cos(2\pi k V_a)$ and $b_3^{(k)}=2 n_X c_3 \sin(2\pi k V_X)$). The analysis extends to Kähler anomalies by couplings to logs of Kähler moduli, showing that full $SL(2,\mathbb{R})$ can be restored for planes not fixed by an order-two twist, while planes fixed by such twists are broken by D5-brane couplings. The work clarifies the duality-based anomaly cancellation in orientifolds, highlights the special role of twisted sectors and linear multiplets, and outlines future tasks for explicit coefficient derivations and phenomenological consequences like Fayet-Iliopoulos terms and anomalous-gauge-boson masses.

Abstract

It has been proposed that gauge and Kaehler anomalies in four-dimensional type IIB orientifolds are cancelled by a generalized Green-Schwarz mechanism involving exchange of twisted RR-fields. We explain how this can be understood using the well-known duality between linear and chiral multiplets. We find that all the twisted fields associated to the N=1 sectors and some of the fields associated to the N=2 sectors reside in linear multiplets. But there are no linear multiplets associated to order-two twists. Only the linear multiplets contribute to anomaly cancellation. This suffices to cancel all U(1) anomalies. In the case of Kaehler symmetries the complete SL(2,R) can be restored at the quantum level for all planes that are not fixed by an order-two twist.