Heterotic String Compactification and New Vector Bundles

TL;DR

This paper introduces new methods for constructing Calabi-Yau manifolds via branched double covers of twistor spaces, enabling heterotic string compactifications with realistic particle physics models.

Contribution

It presents novel constructions of Calabi-Yau manifolds and stable vector bundles suitable for heterotic string theory, expanding the landscape of compactification options.

Findings

Constructed K"ahler and non-K"ahler Calabi-Yau manifolds from twistor spaces.

Developed stable and polystable vector bundles capable of producing three-generation models.

Provided examples of heterotic compactifications with realistic particle physics features.

Abstract

We propose a construction of K\"ahler and non-K\"ahler Calabi-Yau manifolds by branched double covers of twistor spaces. In this construction we use the twistor spaces of four-manifolds with self-dual conformal structures, with the examples of connected sum of $n$ $\mathbb{P}^{2}$s. We also construct $K3$-fibered Calabi-Yau manifolds from the branched double covers of the blow-ups of the twistor spaces. These manifolds can be used in heterotic string compactifications to four dimensions. We also construct stable and polystable vector bundles. Some classes of these vector bundles can give rise to supersymmetric grand unified models with three generations of quarks and leptons in four dimensions.