Moduli restriction and Chiral Matter in Heterotic String Compactifications

TL;DR

This paper explores how discrete twists in heterotic string compactifications can reduce bundle moduli and generate new chiral matter contributions, aiding in more controlled and flexible model building.

Contribution

It provides a concrete example of using discrete twists to restrict moduli and produce additional chiral matter in heterotic string models.

Findings

Discrete twists constrain bundle moduli space.

New contributions of chiral matter are computed.

Enhanced flexibility in heterotic model building.

Abstract

Supersymmetric heterotic string models, built from a stable holomorphic vector bundle $V$ on a Calabi-Yau threefold $X$, usually come with many vector bundle moduli whose stabilisation is a difficult and complex task. It is therefore of interest to look for bundle constructions which, from the outset, have as few as possible bundle moduli. One way to reach such a set-up is to start from a generic construction and to make discrete modifications of it which are available only over a subset of the bundle moduli space. Turning on such discrete 'twists' constrains the moduli to the corresponding subset of their moduli space: the twisted bundle has less parametric freedom. We give an example of a set-up where this idea can be considered concretely. Such non-generic twists lead also to new contributions of chiral matter (which greatly enhances the flexibility in model building); their computation constitutes the main issue of this note.