Superconformal Ward Identities for Green Functions with Multiple Supercurrent Insertions

TL;DR

This paper derives superconformal Ward identities for Green functions with multiple supercurrent insertions in N=1 supersymmetric theories, using superfield formalism to analyze transformation properties and anomalies.

Contribution

It introduces a superfield approach to superconformal Ward identities with multiple insertions, clarifying scheme-independent relations and geometrical anomalies.

Findings

Derived superconformal Ward identities for multiple supercurrent insertions.

Analyzed scheme-independent relations between quasi-local terms and supercurrent correlators.

Connected superfield formalism results to component formalism implications.

Abstract

Superconformal Ward identities for N=1 supersymmetric quantum field theories in four dimensions are convenienty obtained in the superfield formalism by combining diffeomorphisms and Weyl transformations on curved superspace. Using this approach we study the superconformal transformation properties of Green functions with one or more insertions of the supercurrent to all orders in perturbation theory. For the case of two insertions we pay particular attention to fixing the additional counterterms present, as well as to the purely geometrical anomalies which contribute to the transformation behaviour. Moreover we show in a scheme-independent way how the quasi-local terms in the Ward identities are related to similar terms which contribute to the supercurrent two and three point functions. Furthermore we relate our superfield approach to similar studies which use the component formalism by discussing the implications of our approach for the components of the supercurrent and of the supergravity prepotentials.