Generalized Noncommutative Supersymmetry from a New Gauge Symmetry

Using the notion of a gauge connection on a flat superspace, we construct a general class of noncommutative ($D=2,$ $\mathcal{N}=1$) supertranslation algebras generalizing the ordinary algebra by inclusion of some new bosonic and fermionic operators. We interpret the new operators entering into the algebra as the generators of a U(1) (super) gauge symmery of the underlying theory on superspace. These superalgebras are gauge invariant, though not closed in general. We then show that these type of superalgebras are naturally realized in a supersymmetric field theory possessing a super U(1) gauge symmetry. As the non-linearly realized symmetries of this theory, the generalized noncommutative (super)translations and super gauge transformations are found to form a closed algebra.