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

TL;DR

This paper investigates D=2, N=2 supersymmetric sigma models on non(anti)commutative superspace, revealing their complex structure, covariant formulation, and classical properties of gauged linear models with supersymmetry breaking.

Contribution

It extends previous work by showing the non-standard, infinite-term structure of the action and provides a covariant formulation using Kahler normal coordinates, including vector multiplets and supersymmetry transformations.

Findings

Action contains infinite terms depending on non(anti)commutativity parameter

Covariant form of the action achieved with Kahler normal coordinates

Explicit expressions for vector and twisted superfields derived

Abstract

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^{\alpha\beta}. We show that using Kahler 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.