Integer superspin supercurrents of matter supermultiplets

In recent papers [18, 21] we demonstrated that consistent and non-trivial linear transformations of matter supermultiplets generate half-integer superspin supercurrents and the cubic interactions between matter and half-integer superspin supermultiplets. In this work we show that consistent and non-trivial antilinear transformations of matter superfields lead to the construction of integer superspin supercurrents and the cubic interactions between mater and integer superspin supermultiplets. Applying Noether's method to these transformations, we find new integer superspin supercurrents for the case of a free massless chiral superfield. Furthermore, we use them to find new integer superspin supercurrent multiplets for a massive chiral superfield and a chiral superfield with a linear superpotential. Also various selection rules for such interactions are found.