Supersymmetry Anomalies, the Witten Index and the Standard Model

Abstract

The supersymmetric standard model (SSM) contains a wealth of potential supersymmetry anomalies, all of which occur in the renormalization of composite operators of the theory. The coefficients of the weak-E.M. superanomalies should be related to the Witten indices of the neutrino and photon superfields, and the coefficients of the strong superanomalies should be related to the Witten indices of the gluon and photon superfields. Assuming the coefficients are non-zero, the superanomalies break supersymmetry in observable states. However the neutral Higgs particles should remain in a supermultiplet because the Higgs supermultiplet is not coupled to any massless superfield in the SSM. Assuming that the overall Witten index is non-zero, supersymmetry is broken by superanomalies and yet the vacuum remains supersymmetric. This means that the cosmological constant is naturally zero after supersymmetry breaking, even beyond perturbation theory.