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Abstract:

We propose a scenario to stabilize all geometric moduli-that is, the complex structure, Kähler 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 nonperturbative 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 Kähler 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 nonperturbative 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 nonperturbative effects, where all remaining flat directions are stabilized in an anti-de Sitter vacuum. © 2011 American Physical Society.

Abstract:

In this paper, we show that the presence of gauge fields in heterotic Calabi-Yau compactifications can cause the stabilization of some, or all, of the complex structure moduli while maintaining a Minkowski vacuum. Certain deformations of the Calabi-Yau complex structure, with all other moduli held fixed, can lead to the gauge bundle becoming non-holomorphic and, hence, non-supersymmetric. This is manifested by a positive F-term potential which stabilizes the corresponding complex structure moduli. We use 10-and 4-dimensional field theory arguments as well as a derivation based purely on algebraic geometry to show that this picture is indeed correct. An explicit example is presented in which a large subset of complex structure moduli is fixed. We demonstrate that this type of theory can serve as the hidden sector in heterotic vacua with realistic particle physics. © SISSA 2011.