Heterotic Moduli Stabilisation

TL;DR

This paper systematically analyzes moduli stabilization in heterotic string compactifications, proposing mechanisms for fixing moduli, achieving stable vacua, and discussing implications for supersymmetry breaking, gauge unification, and the cosmological constant.

Contribution

It introduces new stable Minkowski and de Sitter vacua in heterotic string theory with stabilized moduli and explores geometric fluxes and non-complex manifolds for tuning physical parameters.

Findings

Stable Minkowski and dS vacua with fixed moduli

Moduli stabilization at large volumes and weak coupling

Potential for gauge coupling unification at 10^16 GeV

Abstract

We perform a systematic analysis of moduli stabilisation for weakly coupled heterotic string theory compactified on manifolds which are Calabi-Yau up to alpha' effects. We review how to fix all geometric and bundle moduli in a supersymmetric way by fractional fluxes, the requirement of a holomorphic gauge bundle, D-terms, higher order perturbative contributions to W, non-perturbative and threshold effects. We then show that alpha' corrections to K lead to new stable Minkowski (or dS) vacua where the complex structure moduli Z and the dilaton are fixed supersymmetrically, while the fixing of the Kahler moduli at a lower scale leads to spontaneous SUSY breaking. The minimum lies at moderately large volumes of all geometric moduli, at a perturbative string coupling and at the right value of the GUT coupling. We also give a dynamical derivation of anisotropic compactifications which allow for gauge coupling unification around 10^16 GeV. The gravitino mass can be anywhere between the GUT and TeV scale depending on the fixing of the Z-moduli. In general, these are fixed by turning on background fluxes, leading to a gravitino mass around the GUT scale since the heterotic 3-form flux does not contain enough freedom to tune W to small values. Moreover accommodating the observed value of the cosmological constant (CC) is a challenge. Low-energy SUSY could instead be obtained in particular situations where the gauge bundle is holomorphic only at a point-like sub-locus of Z-moduli space, or where the number of Z-moduli is small (like orbifold models), since in these cases one may fix all moduli without turning on any quantised flux. However tuning the CC is even more of a challenge in these cases. Another option is to focus on non-complex manifolds since these allow for new geometric fluxes which can be used to tune W and the CC, even if their moduli space is presently only poorly understood.