An effective description of the landscape - II

We continue our analysis of establishing the reliability of "simple" effective theories where massive fields are "frozen" rather than integrated out, in a wide class of four dimensional theories with global or local N = 1 supersymmetry. We extend our previous work by adding gauge fields and O(1) Yukawa-like terms for the charged fields in the superpotential. For generic Kahler potentials, a meaningful freezing is allowed for chiral multiplets only, whereas in general heavy vector fields have to properly be integrated out. Heavy chiral fields can be frozen if they approximately sit to supersymmetric solutions along their directions and, in supergravity, if the superpotential at the minimum is small, so that a mass hierarchy between heavy and light fields is ensured. When the above conditions are met, we show that the simple effective theory is generally a reliable truncation of the full one.