The Generalized Green-Schwarz Mechanism for Type IIB Orientifolds with D3- and D7-Branes

TL;DR

This work develops a comprehensive framework for Type IIB orientifolds on smooth Calabi–Yau threefolds with D3- and D7-branes, deriving detailed tadpole cancellation conditions and a generalized Green–Schwarz mechanism to cancel chiral anomalies. It shows that, in general, cancellations require not only D3 and D7 tadpoles but also the vanishing of induced D5 charges when $h^{1,1}_{-}\neq0$, and extends the analysis to include D9- and D5-branes with a unified method to compute the chiral spectrum. The approach relies on topological data (cycles, Chern characters, fluxes) and yields explicit Green–Schwarz couplings, mass terms, and FI parameters, providing tools to embed local models into compact manifolds and to explore connections to F-theory. Overall, the paper clarifies the interplay between tadpole constraints and anomaly cancellation in a broad class of IIB orientifolds and offers a systematic path to generalize to richer brane configurations.

Abstract

In this paper, we work out in detail the tadpole cancellation conditions as well as the generalized Green-Schwarz mechanism for type IIB orientifold compactifications with D3- and D7-branes. We find that not only the well-known D3- and D7-tadpole conditions have to be satisfied, but in general also the vanishing of the induced D5-brane charges leads to a non-trivial constraint. In fact, for the case $h^{1,1}_{-} \neq 0$ the latter condition is important for the cancellation of chiral anomalies. We also extend our analysis by including D9- as well as D5-branes and determine the rules for computing the chiral spectrum of the combined system.

Figures (1)

• Figure 1: Anomaly and Green-Schwarz diagrams.