Ma. Deandrade et Om. Delcima, SUPER-TAU(3)QED AND THE DIMENSIONAL REDUCTION OF N=1 SUPER-QED(2+2), International journal of modern physics A, 11(8), 1996, pp. 1367-1389
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.