The non-anticommutative supersymmetric Wess-Zumino model

TL;DR

This paper investigates the non-anticommutative supersymmetric Wess-Zumino model in four dimensions, focusing on its algebra, renormalisation up to two loops, and the equivalence of auxiliary field elimination methods.

Contribution

It introduces differential operators for the non-anticommutative supersymmetry algebra and performs two-loop renormalisation, demonstrating the equivalence of auxiliary field elimination methods.

Findings

Successful two-loop renormalisation of the model.

Auxiliary field elimination methods yield equivalent results.

Established the implementation of non-anticommutative algebra on component fields.

Abstract

We discuss the non-anticommutative (N=1/2) supersymmetric Wess-Zumino model in four dimensions. Firstly we introduce differential operators which implement the non-anticommutative supersymmetry algebra acting on the component fields and action. Then we perform the renormalisation of the model up to two-loop order, including the complete set of terms necessary for renormalisability. We show that (at least up to this order) the results obtained when we eliminate the auxiliary field after renormalisation are equivalent to those obtained when we eliminate the auxiliary fields before quantisation.