Bundles over Nearly-Kahler Homogeneous Spaces in Heterotic String Theory

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 $SU(3)\mathrm{/}U(1{)}^2$. This space supports a large number of vector bundles which lead to consistent heterotic vacua, some of them with three chiral families.