Against Supersymmetry

TL;DR

This paper investigates the structure of supersymmetric gauge theories in a quantum framework, proving the uniqueness of the interaction Lagrangian and identifying anomalies at second order, with implications for the standard model.

Contribution

It demonstrates the uniqueness of the SUSY-QCD interaction Lagrangian under natural assumptions and analyzes anomalies appearing at second order in perturbation theory.

Findings

The interaction Lagrangian for massless SUSY non-Abelian gauge theories is uniquely determined.

Anomalies arise at second order in perturbation theory that cannot be eliminated.

Massive and massless bosons must decouple, conflicting with the standard model.

Abstract

We consider the massless supersymmetric vector multiplet in a purely quantum framework and propose a power counting formula. Then we prove that the interaction Lagrangian for a massless supersymmetric non-Abelian gauge theory (SUSY-QCD) is uniquely determined by some natural assumptions, as in the case of Yang-Mills models, however we do have anomalies in the second order of perturbation theory. The result can be easily generalized to the case when massive multiplets are present, but one finds out that the massive and the massless Bosons must be decoupled, in contradiction with the standard model. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make a thorough analysis of the model working only with the component fields.