Heterotic strings on homogeneous spaces

We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS-NS 2-forms and gauge field fluxes. We give the general formalism and modular-invariant partition functions, then we consider some examples such as SU(2)/U(1) ∼ S² (already described in a previous paper) and the SU(3)/U(1)² flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.