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

TL;DR

This paper formulates a two-dimensional N=2 supersymmetric theory on a non(anti)commutative superspace, demonstrating partial supersymmetry preservation and generalizing to include arbitrary superpotentials.

Contribution

It provides the explicit form of the classical action with a general Kähler potential on non(anti)commutative superspace, preserving half of the supersymmetry to all orders.

Findings

Action expressed as a power series in det C

Half of N=2 supersymmetry preserved

Generalization to arbitrary superpotentials

Abstract

The classical action of a two dimensional N=2 supersymmetric theory, characterized by a general K\"{a}hler 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 $C^{\alpha\beta}$. 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.