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We study the duality of the supersymmetric self-dual and Maxwell-Chern-Simonstheories coupled to a fermionic matter superfield, using a master action. Thisapproach evades the difficulties inherent to the quartic couplings that appearwhen matter is represented by a scalar superfield. The price is that thespinorial matter superfield represents a unusual supersymmetric multiplet,whose main physical properties we also discuss.

Equivalence between supersymmetric self-dual and Maxwell-Chern-Simons models coupled to a matter spinor superfield