N = 1 super-τ3QED from Atiyah-Ward space-time

In this letter, we present the action for the massive super-QED2+2. A pair of chiral and a pair of anti-chiral superfields with opposite U(1)-charges are required. We also carry out a dimensional reduction à la Scherk from (2 + 2) to (1 + 2) dimensions, and we show that, after suitable truncations are performed, the supersymmetric extension of the τ3QED1+2 naturally comes out.