D = 2 , N = 2 Supersymmetric σ - models on Non ( anti ) commutative

We extend the results of hep-th/0310137 to show that a general classical action for D = 2, N = 2 sigma models on a non(anti)commutative superspace is not standard and contains infinite number of terms, which depend on the determinant of the non(anti)commutativity parameter, C αβ. We show that using Kähler normal coordinates the action can be written in a manifestly covariant manner. We introduce vector multiplets and obtain the N = 1/2 supersymmetry transformations of the theory in the Wess-Zumino gauge. By explicitly deriving the expressions for vector and twisted superfields on non(anti)commutative superspace, we study the classical aspects of Gauged linear sigma models.