More Dual Fluxes and Moduli Fixing

TL;DR

This work extends flux compactifications by incorporating non-geometric Q fluxes and an S-duality–driven set of P fluxes, restoring T- and S-duality invariance in type II orientifolds and their duals. It derives generalized, duality-covariant superpotentials across IIA/O6, IIB/O3, and IIB/O9 frames, analyzes the resulting tadpoles and Bianchi constraints, and presents explicit Minkowski vacua with moduli stabilization patterns, including dilaton, complex structure, and in some cases Kähler moduli. The authors further develop a unified framework of 128 flux degrees of freedom organized under SL(2,Z)^7, with M-theory and heterotic interpretations via twisted tori, and discuss the implications for complete duality invariance, moduli fixing, and model-building potential. While some moduli remain unfixed within the explored flux classes, the paper highlights a rich landscape of dual fluxes and a path toward fully duality-consistent, moduli-stabilized vacua across multiple string theory corners.

Abstract

We generalize the recent proposal that invariance under T-duality leads to additional non-geometric fluxes required so that superpotentials in type IIA and type IIB orientifolds match. We show that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms. We find new classes of N=1 supersymmetric Minkowski vacua based on type IIB toroidal orientifolds in which not only dilaton and complex moduli but also Kahler moduli are fixed. The chains of dualities relating type II orientifolds to heterotic and M-theory compactifications suggests the existence of yet further flux degrees of freedom. Restricting to a particular type IIA/IIB or heterotic compactification only some of these degrees of freedom have a simple perturbative and/or geometric interpretation.