Conformal Transformation Properties of the Supercurrent in Four Dimensional Supersymmetric Theories

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.

35 pages, AMS-LaTex, four ps figures. Two remarks added, misprints corrected. To be published in Nuclear Physics B

References in corpus (3)

• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• The Supercurrent Trace Identities of the N=1, D=4 Super-Yang-Mills Theory in the Wess-Zumino Gauge

Cited by in corpus (10)

• Four-Dimensional Superconformal Theories with Interacting Boundaries or Defects
• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory
• A non-renormalization theorem for conformal anomalies
• Superconformal Symmetry and Correlation Functions
• Supersymmetry Transformation of Quantum Fields II: Supersymmetric Yang-Mills Theory
• Supersymmetry Transformation of Quantum Fields
• Superconformal Ward Identities for Green Functions with Multiple Supercurrent Insertions
• Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions
• Superconformal Transformation Properties of the Supercurrent II: Abelian Gauge Theories