The effective action of type II Calabi-Yau orientifolds

TL;DR

This work derives the four-dimensional N=1 effective actions for Type II Calabi–Yau orientifolds with background fluxes by a detailed Kaluza–Klein reduction, expressing the Kahler potential, gauge couplings, and flux-induced superpotentials in terms of Calabi–Yau data and fluxes. It establishes a novel link between the chiral description and Hitchin's generalized geometry, and shows how a dual linear-multiplet formulation recovers the underlying N=2 special geometry; in IIB, fluxes yield superpotentials, D-terms, and often a massive linear multiplet, while in IIA the superpotential depends on all geometric moduli. The paper also demonstrates how these orientifolds embed naturally into M-theory and F-theory frameworks and analyzes mirror symmetry in this context, elucidating how instanton actions linearize in the appropriate coordinates. Moreover, it develops the linear-multiplet formalism to expose no-scale structures and discusses D-instanton corrections and potential moduli stabilization, with implications for connecting string compactifications to phenomenology. Overall, the results provide a comprehensive, geometry-driven blueprint for moduli stabilization and duality-consistent embeddings of orientifold compactifications in higher-dimensional theories.

Abstract

This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB Calabi-Yau orientifolds in the presence of background fluxes by using a Kaluza-Klein reduction. The Kahler potential, the gauge kinetic functions and the flux-induced superpotential are determined in terms of geometrical data of the Calabi-Yau orientifold and the background fluxes. As a new result, it is shown that the chiral description directly relates to Hitchin's generalized geometry encoded by special odd and even forms on a threefold, whereas a dual formulation with several linear multiplets makes contact to the underlying N = 2 special geometry. In type IIB setups, the flux-potentials can be expressed in terms of superpotentials, D-terms and, generically, a massive linear multiplet. The type IIA superpotential depends on all geometric moduli of the theory. It is reviewed, how type IIA orientifolds arise as a special limit of M-theory compactified on specific G_2 manifolds by matching the effective actions. In a similar spirit type IIB orientifolds are shown to descend from F-theory on a specific class of Calabi-Yau fourfolds. In addition, mirror symmetry for Calabi-Yau orientifolds is briefly discussed and it is shown that the N = 1 chiral coordinates linearize the appropriate instanton actions.

Figures (3)

• Figure 1: Brane-world scenario on ${\mathbb{M}^{3,1}} \times {Y}$ with space-time filling D-branes, orientifold planes and background fluxes.
• Figure 2: The duality web of String Theories.
• Figure 3: The local moduli space $\mathcal{M}_{\mathbb{R}} = \mathcal{M}_{\mathbb{R}}^{\rm cs} \times \mathbb{R}$ in $\mathcal{M}^{\rm cs} \times \mathbb{C} \simeq \mathcal{M}^{\rm cs} \times H^{(3,0)}$.