Abstract
In this work the supersymmetric gauge-invariant action for the massive Abelian N=1 super-QED 2+2 in the Atiyah-Ward space-time (D=2+2) is formulated. The questions concerning the scheme of the gauge invariance in D=2+2 by means of gauging the massive N=1 super-QED 2+2 are investigated. We study how to ensure the gauge invariance at the expense of the introduction of a complex vector superfield. We discuss the Wess-Zumino gauge and thereupon we conclude that, in this gauge, only the imaginary part of the complex vector field, Bμ, gauges a U(1) symmetry. whereas its real part gauges a Weyl symmetry. We build up the gauge-invariant massive term by introducing a pair of chiral and antichiral superfields with opposite U(1) charges. We carry out a dimensional reduction à la Scherk of the massive N=1 super-QED 2+2 action from D=2+2 to D=1+2. Truncations are needed in order to suppress nonphysical modes, and we end up with a parity-preserving N=1 super-QED 1+2 (rather than N=2) in D=1+2. Finally, we show that the N=1 super-QED 1+2 we have obtained is the supersymmetric version of τ3 QED .
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