The effective action of N=1 Calabi-Yau orientifolds

TL;DR

This work derives the four-dimensional N=1 effective action for Type IIB string theory compactified on Calabi–Yau orientifolds with background fluxes. By performing a systematic Kaluza-Klein reduction and orientifold projections, it computes the Kahler potential, superpotential, and gauge-kinetic functions for two cases: O3/O7 and O5/O9, ensuring consistency with N=1 supergravity. A key finding is a new class of no-scale Kahler potentials, most naturally understood in a dual linear-multiplet formulation, and a detailed account of how fluxes contribute to the F-term and D-term potentials in each case. The analysis reveals that O3/O7 potentials are governed by a GVW-type superpotential independent of Kähler moduli (up to no-scale mixing), while O5/O9 setups feature both superpotential and D-term contributions, with mass terms for linear multiplets arising in the presence of NS flux. The results illuminate the structure of flux vacua and connect to F-theory considerations, with implications for moduli stabilization and brane couplings within a unified N=1 framework.

Abstract

We determine the N=1 low energy effective action for compactifications of type IIB string theory on compact Calabi-Yau orientifolds in the presence of background fluxes from a Kaluza-Klein reduction. The analysis is performed for Calabi-Yau threefolds which admit an isometric and holomorphic involution. We explicitly compute the Kahler potential, the superpotential and the gauge kinetic functions and check the consistency with N=1 supergravity. We find a new class of no-scale Kahler potentials and show that their structure can be best understood in terms of a dual formulation where some of the chiral multiplets are replaced by linear multiplets. For O3- and O7-planes the scalar potential is expressed in terms of a superpotential while for O5- and O9-planes also a D-term and a massive linear multiplet can be present. The relation with the associated F-theory compactifications is briefly discussed.