Non-local Wess-Zumino Model on Nilpotent Noncommutative Superspace

We investigate deformed Wess-Zumino model on N = 1 four dimensional superspace in which bosonic-fermionic noncommutativitiy [x, θ] = iλ is realized. This deformation intertwines ordinary space-time noncommutative field theory and recently proposed N = 1 2 non-(anti)commutative theory. This deformation is nilpotent and we can explicitly evaluate noncommutative effect by means of new interaction between component fields. Difference is that this noncommutativity does break full N = 1 SUSY giving completely broken N = 0 theory for Minkowski signature and deformation terms has Grassmann coupling. Similar to space-time noncommutativity, there cannot help being higher derivative theory and will be non-local. But this non-locality is milder than space-time noncommutative field theory. Due to the nilpotent feature of coupling constant, we can see there are only finite number of Feynman diagrams that gives noncommutative correction at each loop order. E-mail : [email protected] E-mail : [email protected]