Heterotic Strings with Torsion
  In this paper we describe the heterotic dual of the type IIB theory compactified to four dimensions on a toroidal orientifold in the presence of fluxes. The type IIB background is most easily described in terms of an M-theory compactification on a four-fold. The heterotic dual is obtained by performing a series of U-dualities. We argue that these dualities preserve supersymmetry and that the supergravity description is valid after performing them. The heterotic string is compactified on a manifold that is no longer Kahler and has torsion. These manifolds have to satisfy a number of constraints, for example, existence of an holomorphic three-form, size limits, torsional equations etc. We give an explicit form of the background and study the constraints associated to them. 
Katrin Becker, Keshav Dasgupta