Infinite families of homogeneous Bismut Ricci flat manifolds

Starting from compact symmetric spaces of inner type, we provide infinite families of compact homogeneous spaces carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized symmetric spaces of order 4 and (up to coverings) they can be realized as minimal submanifolds of the Bismut flat model spaces, namely compact Lie groups. This construction generalizes the standard Cartan embedding of symmetric spaces.