Supersymmetric CP^N Sigma Model on Noncommutative Superspace

TL;DR

This paper develops a supersymmetric $CP^N$ sigma model on noncommutative superspace, demonstrating its $rac{1}{2}$-supersymmetry and deriving its two-dimensional version via dimensional reduction.

Contribution

It provides a closed-form action for the supersymmetric $CP^N$ sigma model on noncommutative superspace, preserving $rac{1}{2}$-supersymmetry without modifying transformation laws.

Findings

Model exhibits $rac{1}{2}$-supersymmetry.

Transformation law remains unaltered.

Two-dimensional model obtained by dimensional reduction.

Abstract

We construct a closed form of the action of the supersymmetric $CP^N$ sigma model on noncommutative superspace in four dimensions. We show that this model has $\mathcal{N}={1/2}$ supersymmetry and that the transformation law is not modified. The supersymmetric $CP^N$ sigma model on noncommutative superspace in two dimensions is obtained by dimensional reducing the model in four dimensions.