Supersymmetric Field Theories on Noncommutative Spaces

TL;DR

This paper constructs supersymmetric field theories on noncommutative spaces, demonstrating that their supersymmetry algebra and actions are independent of the space's representation and relate closely to the IIB matrix model.

Contribution

It introduces two representations of noncommutative space and shows the supersymmetric Yang-Mills action's independence from these representations.

Findings

Supersymmetry algebra is consistent across different noncommutative space representations.

Supersymmetric Yang-Mills action is independent of the chosen representation.

The action is closely related to the IIB matrix model.

Abstract

Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its representation. As a result, we will see that the action has a close relationship with IIB matrix model.