Superstring compactification on homogeneous coset spaces with torsion

Compactifications of the heterotic string on M⁴×K are investigated, where M⁴ is four- Minkowski spacetime and K is a six-dimensional compact coset manifold with torsion. The β-functions of the underlying two-dimensional nonlinear σ-model, as well as the central charge of the Virasoro algebra, are argued to vanish for K=SU(3)/U(1)×U(1) and G₂/SU(3) with a particular choice of torsion and radius of the manifold. These two coset spaces may provide therefore a perturbative solution of the classical string field equations.