IIA String Theory on Calabi-Yau Fourfolds with Background Fluxes

TL;DR

This paper investigates type IIA string theory compactifications on Calabi-Yau fourfolds with fluxes, deriving the superpotential and demonstrating moduli stabilization and non-supersymmetric vacua.

Contribution

It explicitly derives the superpotential induced by Ramond-Ramond fluxes in type IIA on Calabi-Yau fourfolds using a democratic supergravity formulation.

Findings

All geometric moduli are stabilized by fluxes.

Non-supersymmetric vacua with positive scalar potential are found.

Superpotential matches calibration-based formulas.

Abstract

Looking for string vacua with fixed moduli, we study compactifications of type IIA string theory on Calabi-Yau fourfolds in the presence of generic Ramond-Ramond fields. We explicitly derive the (super)potential induced by Ramond-Ramond fluxes performing a Kaluza-Klein reduction of the ten-dimensional effective action. This can be conveniently achieved in a formulation of the massive type IIA supergravity where all Ramond-Ramond fields appear in a democratic way. The result agrees with the general formula for the superpotential written in terms of calibrations. We further notice that for generic Ramond-Ramond fluxes all geometric moduli are stabilized and one finds non-supersymmetric vacua at positive values of the scalar potential.