The effective action of Type IIA Calabi-Yau orientifolds

TL;DR

This work derives the 4D N=1 effective action for generic Type IIA Calabi-Yau orientifolds with background fluxes via a Kaluza-Klein reduction, identifying the Kahler potentials for the Kahler and complex-structure-like sectors and the holomorphic gauge-kinetic functions. The fluxes generate a flux-induced superpotential that depends on all geometric moduli, splitting into NS- and RR-sector contributions, and instanton effects are shown to linearly couple to the N=1 coordinates, allowing holomorphic corrections. The orientifold configuration is linked to M-theory on special G2 manifolds, with an explicit matching of moduli spaces and couplings, and mirror symmetry is analyzed in the large volume/large complex structure limit, yielding a consistent map between IIA orientifolds and their IIB mirrors in both Kahler and complex-structure sectors. The results provide a coherent framework for moduli stabilization, including potential nonperturbative corrections from worldsheet and D-brane instantons, and reveal the geometric structure of the N=1 moduli space via a Legendre transform and links to Hitchin-type moduli of Lagrangian submanifolds.

Abstract

The N=1 effective action for generic type IIA Calabi-Yau orientifolds in the presence of background fluxes is computed from 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. The moduli space is found to be a Kahler subspace of the N=2 moduli space and shown to coincide with the moduli space arising in compactification of M-theory on a specific class of G_2 manifolds. The superpotential depends on all geometrical moduli and vanishes at leading order when background fluxes are turned off. The N=1 chiral coordinates linearize the appropriate instanton actions such that instanton effects can lead to holomorphic corrections of the superpotential. Mirror symmetry between type IIA and type IIB orientifolds is shown to hold at the level of the effective action in the large volume - large complex structure limit.