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.Comment: D.Phil. thesis, 143pages, twosid
