Field Theory on Nonanticommutative Superspace

TL;DR

This paper explores a specific deformation of supersymmetry algebra using a twist, leading to a noncommutative star-product in Minkowski space, affecting superfield structures and the Wess-Zumino action.

Contribution

It introduces a novel twist-based deformation of SUSY Hopf algebra in Minkowski space, analyzing its impact on superfields and the Wess-Zumino model.

Findings

Deformed Leibniz rule for SUSY transformations derived.

Star-product is noncommutative, hermitian, and finite.

Chiral superfields are no longer a subalgebra.

Abstract

We discuss a deformation of the Hopf algebra of supersymmetry (SUSY) transformations based on a special choice of twist. As usual, algebra itself remains unchanged, but the comultiplication changes. This leads to the deformed Leibniz rule for SUSY transformations. Superfields are elements of the algebra of functions of the usual supercoordinates. Elements of this algebra are multiplied by using a $\star$-product which is noncommutative, hermitian and finite when expanded in power series of the deformation parameter. Chiral fields are no longer a subalgebra of the algebra of superfields. One possible deformation of the Wess-Zumino action is proposed and analysed in detail. Differently from most of the literature concerning this subject, we work in Minkowski space-time.