Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua

TL;DR

This paper demonstrates that gauge fields in heterotic Calabi-Yau compactifications can stabilize complex structure moduli, leading to more controlled and realistic string vacua with potential applications in particle physics.

Contribution

It provides a novel mechanism showing how gauge fields stabilize complex structure moduli in heterotic Calabi-Yau vacua, supported by algebraic geometry and field theory arguments.

Findings

Certain complex structure deformations lead to non-holomorphic gauge bundles.

A large subset of moduli can be stabilized in explicit examples.

The mechanism can serve as a hidden sector compatible with particle physics.

Abstract

In this paper, we show that the presence of gauge fields in heterotic Calabi-Yau compacitifications causes the stabilisation of some, or all, of the complex structure moduli of the Calabi-Yau manifold 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 leads to an 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 and can co-exist with realistic particle physics.