Higgs mechanism for Kalb-Ramond gauge field

Kalb-Ramond gauge field theory, coupled to manifestly gauge-invariant and reparametrization-invariant second-quantized string fields, is studied. String condensation into the vacuum is shown to develop masses to the Kalb-Ramond gauge field which we call the string Higgs mechanism. In case the Kalb-Ramond field couples to the open strings which have a massless vector field in the spectrum, our field theory also exhibits the well-known Stueckelberg mechanism. To strengthen our conclusion, we construct a lattice version of the above string field theory and demonstrate that the mean-field approximation indicates the existence of the Higgs phase