Super Yang-Mills Theory from a Supermatrix Model

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.