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We study the problem of moduli stabilisation in explicit heterotic orbifoldcompactifications, whose spectra contain the MSSM plus some vector-like exoticsthat can be decoupled. Considering all the bulk moduli, we obtain the 4D lowenergy effective action for the compactification, which has contributions fromvarious, computable, perturbative and non-perturbative effects. Hidden sectorgaugino condensation and string worldsheet instantons result in a combinationof racetrack, KKLT and cusp-form contributions to the superpotential, whichlift all the bulk moduli directions. We point out the properties observed inour concrete models, which tend to be missed when only "generic" features of amodel are assumed. We search for interesting vacua and find several de Sittersolutions, but -- so far -- they all turn out to be unstable.

On Moduli Stabilisation and de Sitter Vacua in MSSM Heterotic Orbifolds