N = 1 super-Chern-Simons coupled to parity-preserving matter from Atiyah-Ward space-time

In this letter, we present the Parkes-Siegel formulation for the massive Abelian N = 1 super-QED2+2 coupled to a self-dual supermultiplet, by introducing a chiral multiplier superfield. We show that after carrying out a suitable dimensional reduction from (2 + 2) to (1 + 2) dimensions, and performing some necessary truncations, the simple supersymmetric extension of the τ3QED1+2 coupled to a Chern-Simons term naturally comes out.