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arXiv · hep-th/9501002

Super-$τ_{3}$QED and the dimensional reduction of $N$$=$$1$ super-{QED}$_{2+2}$

M. A. de Andrade·O. M. Del Cima
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Abstract

In this work the supersymmetric gauge invariant action for the massive Abelian $N$$=$$1$ super-{\QED} in the Atiyah-Ward space-time ({\DDdd}) is formulated. The questions concerning the scheme of the gauge invariance in {\DDdd} by means of gauging the massive $N$$=$$1$ super-{\QED} are investigated. We study how to ensure the gauge invariance at the expenses 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, $B_{\m}$, 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 anti-chiral superfields with opposite $U(1)$-charges. We carry out a dimensional reduction {\it{à la}} Scherk of the massive $N$$=$$1$ super-{\QED} action from {\DDdd} to {\Ddd}. Truncations are needed in order to suppress non-physical modes and one ends 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 got is the supersymmetric version ofthe $τ_{3}$QED .

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M. A. de Andrade, O. M. Del Cima. 1995-07-06. Super-$τ_{3}$QED and the dimensional reduction of $N$$=$$1$ super-{QED}$_{2+2}$. https://doi.org/10.1142/s0217751x96000638

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