Quantum Deformations of Space-Time SUSY and Noncommutative Superfield Theory

TL;DR

This paper reviews quantum deformations of supersymmetry, focusing on the $mbda$-deformation of Poincare9 supersymmetry and its implications for noncommutative superfield theory, including star product multiplication and deformed chiral vertices.

Contribution

It introduces a star product for chiral superfields and proposes an integration formula for $mbda$-deformed chiral superspace, advancing the understanding of noncommutative supersymmetric theories.

Findings

Describes the $mbda$-deformation of D=4 Poincare9 supersymmetry.

Develops the star product multiplication for chiral superfields.

Proposes an integration formula over $mbda$-deformed chiral superspace.

Abstract

We review shortly present status of quantum deformations of Poincar\'{e} and conformal supersymmetries. After recalling the $\kappa$-deformation of $\hbox{D=4}$ Poincar\'{e} supersymmetries we describe the corresponding star product multiplication for chiral superfields. In order to describe the deformation of chiral vertices in momentum space the integration formula over $\kappa$-deformed chiral superspace is proposed.