On holomorphic dependence and infrared effects in supersymmetric gauge theories

According to general theorems in supersymmetric gauge theories the chiral quantities should depend on the chiral parameters in a holomorphic way. By chiral parameters we mean the complex coefficients in front of the chiral structures such as the mass parameters of the matter fields or the gauge coupling constant. Actually, this general assertion is often broken if the effective action under consideration contains massless (light) fields. We discuss this phenomenon and show that the violation of holomorphicity can be traced back to the renormalization of the massless fields. It is just their Z-factors that introduce non-holomorphicity explicitly. In some cases it is possible to define quantities which are free from infrared effects violating holomorphicity. We believe that these latter quantities have direct physical meaning and restore holomorphicity. The dependence of the gluino condensate on the gauge coupling constant and the renormalization of the θ-angle are considered as instructive examples.