Supersymmetry

Abstract

In the previous chapter it was shown that in trying to eliminate quadratic divergences in two- and one-point functions of a scalar field one is led to postulate an equal number of bosonic and fermionic d.o.f., as well as specific relations among the couplings in the theory. (Uniqueness was achieved once the relations were required to be scale invariant.) From the consideration of the scalar-vector interaction one is led to postulate new gauge-Yukawa and gauge-quartic interactions. From the consideration of a (non-gauge) Yukawa interaction one is able to fix the scalar trilinear and quartic couplings. These relations suggest a small number of fundamental couplings, and hence a small number of fundamental (super)fields: Fermions and bosons may be arranged in spin multiplets, the superfields, which interact with each other. In this (supersymmetric) language the Lagrangian will contain a small number of terms. Nevertheless, when rewriting the interactions and kinetic terms in terms of the superfield components - the individual boson and fermion fields - the Lagrangian will contain a large number of terms which exhibit what may naively seem to be mysterious correlations.