Generalized Compactification in Heterotic String Theory
  In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that heterotic compactifications on half-flat mirror manifolds are based on this class of solutions.   Furthermore, within this context, we construct specific examples based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our solutions are based on three specific group coset spaces satisfying the half-flat torsion class conditions. It is shown how to construct line bundles over these manifolds, compute their properties and build up vector bundles consistent with supersymmetry and the heterotic anomaly cancellation. It turns out that the most interesting solutions are obtained from $SU(3)/U(1)^2$. This space supports a large number of vector bundles leading to consistent heterotic vacua with GUT group and, for some of them, with three chiral families. 
Cyril Matti
hep-th