Supersymmetric extension of Moyal algebra and its application to the matrix model

TL;DR

This paper develops a supersymmetric extension of the Moyal algebra incorporating fermionic fields and applies it to a matrix model, enabling a unified treatment of gauge and outer degrees of freedom.

Contribution

It introduces a supersymmetric operator representation of Moyal algebra and applies it to matrix models, advancing the understanding of noncommutative geometry in supersymmetric contexts.

Findings

Operator representation of Moyal algebra with fermionic fields

Unified treatment of gauge and outer degrees of freedom in matrix models

Framework for supersymmetric noncommutative geometry

Abstract

We construct operator representation of Moyal algebra in the presence of fermionic fields. The result is used to describe the matrix model in Moyal formalism, that treat gauge degrees of freedom and outer degrees of freedom equally.