Supersymmetric compactifications of heterotic strings with fluxes and condensates

We discuss supersymmetric compactifications of heterotic strings in the presence of H-flux and general condensates using the formalism of G-structures and intrinsic torsion. We revisit the examples based on nearly-Kähler coset spaces and show that supersymmetric solutions, where the Bianchi identity is satisfied, can be obtained when both gaugino and dilatino condensates are present.