On Moduli Stabilisation and de Sitter Vacua in MSSM Heterotic Orbifolds

TL;DR

The paper tackles moduli stabilization in explicit heterotic orbifold compactifications that realize MSSM-like spectra. It develops a full 4D ${ c=1}$ supergravity framework for a realistic $ c Z_{6}$--II MSSM, incorporating gaugino condensation, worldsheet instantons, modular anomalies, and threshold corrections, then analyzes the combined effects on all bulk moduli ($S,T_i,U$). Two concrete models with three Kähler moduli, one complex structure modulus, and the dilaton are studied, yielding superpotentials that fuse racetrack, KKLT, and cusp-form mechanisms; the eta-function thresholds are central to achieving moduli stabilization. Numerically, several de Sitter vacua are found, but all exhibit instabilities or problematic flat directions, indicating that metastable dS vacua remain challenging in these explicit heterotic constructions. The work highlights the intricate interdependence of moduli, exotics decoupling, and modular structure in determining vacua, and it informs future directions for achieving robust metastable de Sitter solutions in string compactifications.

Abstract

We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering all the bulk moduli, we obtain the 4D low energy effective action for the compactification, which has contributions from various, computable, perturbative and non-perturbative effects. Hidden sector gaugino condensation and string worldsheet instantons result in a combination of racetrack, KKLT and cusp-form contributions to the superpotential, which lift all the bulk moduli directions. We point out the properties observed in our concrete models, which tend to be missed when only "generic" features of a model are assumed. We search for interesting vacua and find several de Sitter solutions, but -- so far -- they all turn out to be unstable.