Self-Dual Vector Multiplet in 3D with Gauged Scale Covariance

We present non-trivial interactions of N=1 self-dual massive vector multipletin three-dimensions, with gauged scale covariance. Our multiplets are a vectormultiplet (A_\mu, \lambda) and a gauge multiplet (B_\mu, \chi), where thelatter is used for the gauging of the scale covariance of the former. Due totheabsence of supergravity, this system has no lagrangian formulation, but hasonly a set of field equations. The gauge multiplet can also haveDirac-Born-Infeld type interactions, even in the presence of the massiveself-dual vector multiplet. As a by-product, we also show that scale covariantcouplings are possible for scalar multiplet. We also try a mechanism ofspontaneous breaking of scale covariance by introducing a superpotential forscalar multiplets.Comment: Latex file, 13 pages, no figures, Ref. [12] update