D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace

The classical action of a two dimensional N=2 supersymmetric theory, characterized by a general Kähler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant of the non(anti)commutativity parameter $C^{αβ}$. The theory is explicitly shown to preserve half of the N=2 supersymmetry, to all orders in (det C)^n. The results are further generalized to include arbitrary superpotentials as well.

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