N=1 Super-$\tau_{3}$QED from Atiyah-Ward Space-Time
  In this letter, we present the action for the massive super-{\QED}. 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 {\it{\`a la}} Scherk from (2+2) to (1+2) dimensions, and we show that, after suitable truncations are performed, the supersymmetric extension of the ${\tau}_{3}$QED$_{1+2}$ naturally comes out. 
M. A. De Andrade, O. M. Del Cima