Remarks on a $B \wedge F$ model with topological mass from gauging spin

Aspects of screening and confinement are reassessed for a $B \wedge F$ model with topological mass with the gauging of spin. Our discussion is carried out using the gauge-invariant, but path-dependent, variables formalism. We explicitly show that the static potential profile is the sum of a Yukawa and a linear potential, leading to the confinement of static external charges. Interestingly enough, similar results are obtained in a theory of antisymmetric tensor fields that results from the condensation of topological defects as a consequence of the Julia-Toulouse mechanism.