Field Theories with Global Supersymmetry

Abstract

To apply supersymmetry to describe particle interaction we have to construct field theories that are invariant under supersymmetry transformations. We will then obtain certain constraints among the parameters of the bosonic and fermionic sectors of the theory and compare them with observations. The kind of field theories we are interested in will involve matter fields, which will be given by the chiral superfields and gauge fields, which in turn will be given by the real gauge superfield V. We will always work in the Wess-Zumino gauge for V. These matter and gauge superfields may (and, in general, will) belong to some irreducible representations of compact internal symmetry groups (local or global). Before going on to the discussion of the most general case, we first consider the simple case of a matter field Φ and illustrate how we can write a general interacting field theory for this.