Conformal Transformation Properties of the Supercurrent in Four Dimensional Supersymmetric Theories

TL;DR

This paper studies how the supercurrent in four-dimensional N=1 supersymmetric theories transforms under superconformal symmetries, deriving Ward identities and analyzing potential quantum anomalies using perturbative methods.

Contribution

It provides a detailed analysis of the superconformal transformation properties of the supercurrent and establishes the absence of additional superconformal anomalies in the massless Wess-Zumino model.

Findings

Derived flat space superconformal Ward identities from curved superspace transformations.

Identified the standard dilatational anomalies via a local Callan-Symanzik equation.

Showed no additional superconformal anomalies involving dynamical fields are present.

Abstract

We investigate the superconformal transformation properties of Green functions with one or more insertions of the supercurrent in N=1 supersymmetric quantum field theories. These Green functions are conveniently obtained by coupling the supercurrent and its trace to a classical supergravity background. We derive flat space superconformal Ward identities from diffeomorphisms and Weyl transformations on curved superspace. For the classification of potential quantum superconformal anomalies in the massless Wess-Zumino model on curved superspace a perturbative approach is pursued, using the BPHZ scheme for renormalisation. By deriving a local Callan-Symanzik equation the usual dilatational anomalies are identified and it is shown that no further superconformal anomalies involving the dynamical fields are present.