On image supergravity and projective superspace: Dual formulations Original Research Article

The superspace formulation for four-dimensional image matter-coupled supergravity recently developed in [S.M. Kuzenko, U. Lindström, M. Roček, G. Tartaglino-Mazzucchelli, 4D image supergravity and projective superspace, ] makes use of a new type of conformal compensator with infinitely many off-shell degrees of freedom: the so-called covariant weight-one polar hypermultiplet. In the present note we prove the duality of this formulation to the known minimal image off-shell realization for image Poincaré supergravity involving the improved tensor compensator. Within the latter formulation, we present new off-shell matter couplings realized in terms of covariant weight-zero polar hypermultiplets. We also elaborate upon the projective superspace description of vector multiplets in image conformal supergravity. An alternative superspace representation for locally supersymmetric chiral actions is given. We present a model for massive improved tensor multiplet with both “electric” and “magnetic” types of mass terms.