We have examined the spontaneous breakdown of fermion-number-conserving supersymmetry. In the tree approximation the vacuum expectation values of the difermion fields play a passive role, the values of the potential at the minima being entirely determined by the vacuum expectation values of the usual boson fields. One-loop calculations for three different models show that the vacuum expectation values of the difermion fields should be zero at the potential minima. Our general conjecture is that spontaneous breakdown of fermion number cannot accompany the spontaneous breakdown of supersymmetry.

• Received 13 April 1976

DOI:https://doi.org/10.1103/PhysRevD.14.3548