Some Aspects of Deformations of Supersymmetric Field Theories

Abstract

We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a four dimensional supersymmetric field theory which is the deformation of the Wess-Zumino renormalizable theory of a chiral superfield. We then consider the deformation of a free theory of an abelian vector multiplet, which is a non commutative version of the rank one Yang-Mills theory. We finally give the supersymmetric version of the ${\alpha }^{\prime }\mapsto 0$ limit of the Born-Infeld action with a B-field turned on, which is believed to be related to the non commutative U(1) gauge theory.

arXiv commentAMS LaTeX, 24 pages. References added, some misprints corrected

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