Super Yang-Mills Theory from a Supermatrix Model

TL;DR

This paper develops a supermatrix model framework that derives four-dimensional N=1, N=2, and N=4 super Yang-Mills theories, introducing a new non-anti-commutative superspace for these constructions.

Contribution

It presents a novel supermatrix model approach to derive various super Yang-Mills theories, extending previous non-commutative space methods to supersymmetric cases.

Findings

Constructed a supermatrix model for D=4 N=1 super Yang-Mills.

Extended the model to include matter supermatrices for N=2 and N=4 theories.

Introduced a new non-anti-commutative superspace for field theory formulations.

Abstract

It is known that Yang-Mills theories on non-commutative space can be derived from large-N reduced models. Gauge fields in non-commutative Yang-Mills theories can be described as fluctuations of matrices expanded about an appropriate classical solution of the reduced models. We investigate a generalization of this procedure in superfield formalism. We show that we can construct a supermatrix model such that D=4 $\N=1$ super Yang-Mills theory can be derived from it. In addition, we can couple matter supermatrices to this supermatrix model and also construct models corresponding to $\N=2$ and $\N=4$ super Yang-Mills theories. In these investigations, we need to introduce a new non-anti-commutative superspace, and we investigate the definition of field theories on this space.