Reinterpreting Supersymmetry

Abstract

The mathematically elegant and promising idea of supersymmetry faces severe challenges as its conventional weak-scale realizations are increasingly constrained by the lack of experimental evidence of superpartners. However, we point out that the prediction of new (seemingly non-existing) supersymmetric particles is not a necessity: if we slightly relax our expectations from the supersymmetric models, generators $Q_{\alpha }^a$ of $N$-extended supersymmetry can be readily interpreted as carrying a quantum number of the internal gauge group, thus connecting particles with different gauge properties. In this view, operators $Q_{\alpha }^a$ remain ``square roots'' of translations, but do not by themselves generate symmetries of the model. They merely represent transformations that mathematically relate bosonic and fermionic fields; it is only the gauge-invariant combinations of the form ${\sum }_a\{Q_{\alpha }^a,{\bar{Q}}_{a\beta }\}$ that correspond to spacetime momenta and thus represent symmetries of the model. With this conceptual modification, the simplest Yang-Mills supersymmetric model no longer connects vector bosons with hypothetical gauginos, but with far less exotic chiral fermions, e.g.\ with left-handed leptons. Further adding an $SU(2)$ doublet of Higgs scalars no longer introduces Higgsinos, but a fermion that naturally corresponds to the right-handed lepton, with the familiar Yukawa term showing up as a mathematical necessity. Despite giving up the requirement that operators $Q_{\alpha }^a$ alone generate symmetries of the action, this approach to supersymmetry is strikingly mathematically similar to standard SUSY, raising hopes that many of the favorable properties of standard supersymmetry can be retained, while potentially reconciling the idea of supersymmetry with experimental data. The approach is still quite restrictive: the relative coefficients of such models are strongly determined.