ABSTRACT
When potentially realistic supersymmetric theories are constructed, the chiral superfields discussed in this chapter provide the matter fields, i.e. the quarks, leptons and Higgs scalars and associated with them in the same multiplet their supersymmetric partners, which in the case of the quarks and leptons are the scalar squarks and sleptons and in the case of the Higgses are the fermionic Higgsinos. This chapter uses supersymmetric covariant derivatives to construct the chiral superfield whose component fields form the chiral supermultiplet. It discusses how supersymmetry breaking may arise by spontaneous breakdown of symmetry in a theory with a supersymmetric Lagrangian. The chapter considers first ways of recognizing when supersymmetry is spontaneously broken. The tree level effective potential for supersymmetric theories of chiral superfields has the remarkable property of being positive semi-definite.
