Based on a joint work with D. Bahns and K. Rejzner, I describe the quantization of submanifold embeddings in the sense of an effective field theory, derived from (generalizations of) the Nambu-Goto action. Diffeomorphism invariance is dealt with in the Batalin-Vilkovisky formalism. It is shown that localized observables exist, and that there are no anomalies, for any dimension of source or target space. As an outlook, I describe first steps towards the inclusion of boundaries.