We conjecture the existence of a duality between heterotic closed strings on homogeneous spaces and symmetry-preserving D-branes on group manifolds, based on the observation about the coincidence of the low-energy field description for the two theories. For the closed string side we also give an explicit proof of a no-renormalization theorem as a consequence of a hidden symmetry and infer that the same property should hold true for the higher order terms of the DBI action.