Field theory on nonanticommutative superspace

Abstract

We discuss a deformation of the Hopf algebra of supersymmetry (SUSY) transformations based on the special choice of twist. As usual, algebra itself remains unchanged, but the comultiplication changes. This leads to the deformed Leibniz rule for SUSY transformations. Superfields are elements of the algebra of functions of the usual supercoordinates. Elements of this algebra are multiplied by using the -product which is noncommutative, hermitian and finite when expanded in power series of the deformation parameter. Chiral fields are no longer a subalgebra of the algebra of superfields. One possible deformation of the Wess-Zumino action is proposed and analyzed in detail. Differently from most of the literature concerning this subject, we work in Minkowski space-time. © SISSA 2007.