Stabilizing All Geometric Moduli in Heterotic Calabi-Yau Vacua

TL;DR

This paper presents a method to stabilize all geometric moduli in heterotic Calabi-Yau compactifications without flux, using gauge bundles and non-perturbative effects, leading to fully stabilized Minkowski or AdS vacua.

Contribution

It introduces a novel approach combining gauge bundle effects and non-perturbative corrections to stabilize all moduli in heterotic string theory without flux.

Findings

All complex structure moduli can be perturbatively stabilized.

Remaining Kahler moduli and dilaton can be stabilized with non-perturbative effects.

A specific example achieves complete stabilization in an AdS vacuum.

Abstract

We propose a scenario to stabilize all geometric moduli - that is, the complex structure, Kahler moduli and the dilaton - in smooth heterotic Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is accomplished using the gauge bundle required in any heterotic compactification, whose perturbative effects on the moduli are combined with non-perturbative corrections. We argue that, for appropriate gauge bundles, all complex structure and a large number of other moduli can be perturbatively stabilized - in the most restrictive case, leaving only one combination of Kahler moduli and the dilaton as a flat direction. At this stage, the remaining moduli space consists of Minkowski vacua. That is, the perturbative superpotential vanishes in the vacuum without the necessity to fine-tune flux. Finally, we incorporate non-perturbative effects such as gaugino condensation and/or instantons. These are strongly constrained by the anomalous U(1) symmetries which arise from the required bundle constructions. We present a specific example, with a consistent choice of non-perturbative effects, where all remaining flat directions are stabilized in an AdS vacuum.