Bundles over Nearly-Kahler Homogeneous Spaces in Heterotic String Theory

TL;DR

This paper constructs heterotic string vacua using nearly-Kahler homogeneous spaces, focusing on specific coset spaces, and demonstrates the creation of vector bundles that satisfy supersymmetry and anomaly cancellation, resulting in models with realistic features.

Contribution

It introduces methods to build vector bundles over nearly-Kahler coset spaces, especially $SU(3)/U(1)^2$, for heterotic string compactifications, with explicit constructions and properties.

Findings

Constructed heterotic vacua on three coset spaces.

Identified vector bundles supporting three chiral families.

Demonstrated anomaly cancellation and supersymmetry conditions.

Abstract

We construct heterotic vacua based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our examples are based on three specific group coset spaces. It is shown how to construct line bundles over these spaces, compute their properties and build up vector bundles consistent with supersymmetry and anomaly cancelation. It turns out that the most interesting coset is $SU(3)/U(1)^2$. This space supports a large number of vector bundles which lead to consistent heterotic vacua, some of them with three chiral families.