The effective action of Type IIA Calabi-Yau orientifolds

TL;DR

This paper derives the N=1 effective action for Type IIA Calabi-Yau orientifolds with fluxes, detailing the moduli space, superpotential, and mirror symmetry, providing insights into flux compactifications and instanton effects.

Contribution

It presents a comprehensive calculation of the effective action, including the Kahler potential, gauge kinetic functions, and superpotential, and explores mirror symmetry in flux compactifications.

Findings

Moduli space is a Kahler subspace of N=2 moduli space.

Superpotential depends on all geometrical moduli and vanishes without fluxes.

Mirror symmetry holds at the effective action level in specific limits.

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.