SUPER-TAU(3)QED AND THE DIMENSIONAL REDUCTION OF N=1 SUPER-QED(2+2)

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 inva riance in D = 2 + 2 by means of gauging the massive N = 1 super-QED(22) are investigated. We study how to ensure the gauge invariance at th e expense of the introduction of a complex vector superfield. We discu ss the Wess-Zumino gauge and thereupon we conclude that, in this gauge , only the imaginary part of the complex vector field, B-mu, 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 an d antichiral superfields with opposite U(1) charges. We carry out a di mensional reduction a la Scherk of the massive N = 1 super-QED(2+2) ac tion from D = 2 + 2 to D = 1 + 2. Truncations are needed in order to s uppress 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 th at the N = 1 super-QED(1+2) we have obtained is the supersymmetric ver sion of tau(3)QED.