On-shell Supersymmetry Anomalies and the Spontaneous Breaking of Gauge Symmetry

Abstract

A search for supersymmetry anomalies requires an examination of the BRS cohomology of supersymmetric Yang-Mills coupled to chiral matter, and the physically interesting (on-shell) anomalies are those which cannot be eliminated using the equations of motion. An analysis of this cohomology problem shows that the simplest situation where a physically interesting supersymmetry anomaly can arise is when: 1. the anomaly occurs in the renormalization of a composite antichiral spinor superfield operator constructed from the chiral matter in the theory, 2. the anomalous diagrams are one-loop triangle diagrams containing a gauge propagator, 3. the gauge symmetry (but not supersymmetry) is spontaneously broken, 4. the initial operator has a dimension such that the triangle diagram is at least linearly divergent, 5. the anomaly contains only massless chiral superfields, although (apparently harder to calculate) supersymmetry anomalies can also contain massive chiral superfields, 6. the theory contains vertices which, after gauge symmetry breaking, couple massless matter fields to massive matter fields and massive gauge fields, like the $ e^- \n_e W^+$ vertices of the standard model. The supersymmetry anomalies considered here are all `soft', in the sense that they must vanish when certain masses go to zero. It appears that the order parameter of the resulting supersymmetry breaking may be the vacuum expectation value that breaks the gauge symmetry. Nonzero values for the anomalies, if they exist, appear to generate supersymmetry breaking for observable particles with a cosmological constant that is naturally zero.