  We analyze to all perturbative orders the properties of two possible quantum
extensions of classically on-shell equivalent antisymmetric tensor gauge models
in four dimensions. The first case, related to the soft breaking of a
topological theory wants a gauge field of canonical dimension one. The other
possibility, which assigns canonical dimension two to the gauge field, leads to
the $\sigma$ model interpretation of the theory. In both instances we find that
the models are anomaly free.
