A Note on Superfields and Noncommutative Geometry

TL;DR

This paper develops supersymmetric field theories on noncommutative R^4 using superspace formalism, constructing actions for various gauge and matter multiplets, and discusses auxiliary field derivatives.

Contribution

It introduces a method to formulate N=1 supersymmetric actions on noncommutative space, including multiple gauge groups and matter representations, using superspace formalism.

Findings

Constructed supersymmetric actions for U(N) gauge theories on noncommutative R^4.

Extended the formalism to include product gauge groups and bi-fundamental matter.

Discussed issues related to derivative terms of auxiliary fields in the noncommutative setting.

Abstract

We consider the supersymmetric field theories on the noncommutative $R^4$ using the superspace formalism on the commutative space. The terms depending on the parameter of the noncommutativity $\Theta$ are regarded as the interactions. In this way we construct the N=1 supersymmetric action for the U(N) vector multiplets and chiral multiplets of the fundamental, anti-fundamental and adjoint representations of the gauge group. The action for vector multiplets of the products gauge group and its bi-fundamental matters is also obtained. We discuss the problem of the derivative terms of the auxiliary fields.