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Composite Operators, Supersymmetry Anomalies and Supersymmetry Breaking in the Wess-Zumino Model

John Dixon
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Abstract

The field equations of the auxiliary fields are nonlinear and free of derivatives. Hence, it is argued, a Legendre transform to generate the 1PI Generating Functionals is not correct for the auxiliary fields. A corrected formulation of the BRS symmetry must be constructed by integrating the auxiliary fields. This necessarily destroys manifest supersymmetry. It also generates a new "Physical BRS-ZJ" cohomology problem. The resulting "Physical BRS-ZJ cohomology" is then described. The cohomology contains a rich spectrum of potential supersymmetry anomalies in certain composite operators that have spinor indices. Some examples of these composite operators are set out explicitly. The examples depend on certain Constraint Equations that arise from simple Generating Functions. The Constraint Equations constrain the mass and Yukawa coefficients of the theory. The potential supersymmetry anomalies have calculable one-loop coefficients that depend on the solutions to the Constraint Equations. If these coefficients are non-zero, the anomalies will then necessarily break supersymmetry with a calculable pattern, probably with a zero cosmological constant.

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John Dixon. 2003-03-17. Composite Operators, Supersymmetry Anomalies and Supersymmetry Breaking in the Wess-Zumino Model. https://arxiv.org/abs/hep-th/0303145

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