Superconformal Ward Identities for Green Functions with Multiple Supercurrent Insertions

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.

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Cited by in corpus (10)

• Four-Dimensional Superconformal Theories with Interacting Boundaries or Defects
• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• A non-renormalization theorem for conformal anomalies
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• Supersymmetry Transformation of Quantum Fields II: Supersymmetric Yang-Mills Theory
• Supersymmetry Transformation of Quantum Fields
• Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions
• Superconformal Transformation Properties of the Supercurrent II: Abelian Gauge Theories
• Conformal Transformation Properties of the B-type Supercurrent
• The Conformal Anomaly Action to Fourth Order (4T) in $d=4$ in Momentum Space