Towards Minkowski Vacua in Type II String Compactifications

TL;DR

The article develops a framework to realize perturbative Minkowski vacua with all moduli stabilised in Type II string theory via orientifolds with SU(3)×SU(3) structure, employing generalized geometry to accommodate non-geometric fluxes. By introducing a covariant derivative that captures $H$- and $Q$-fluxes, it derives 4D superpotentials for IIA and IIB and establishes a mirror map between the two pictures, showing that Minkowski vacua with stabilized moduli exist when non-geometric fluxes are present and at least one complex structure modulus is available. The authors present explicit vacua for models with one, two, and three Kähler moduli, with moduli values that can be made parametrically large while preserving tadpole constraints, and they discuss the 10D uplift to twisted generalized Calabi–Yau backgrounds. This work thus provides a concrete route to perturbative, stable Minkowski vacua in string theory, highlighting the utility of generalized geometry in exploring non-geometric compactifications and their phenomenological implications.

Abstract

We study the vacuum structure of compactifications of type II string theories on orientifolds with SU(3)xSU(3) structure. We argue that generalised geometry enables us to treat these non-geometric compactifications using a supergravity analysis in a way very similar to geometric compactifications. We find supersymmetric Minkowski vacua with all the moduli stabilised at weak string coupling and all the tadpole conditions satisfied. Generically the value of the moduli fields in the vacuum is parametrically controlled and can be taken to arbitrarily large values.