An Effective Description of the Landscape - I

Understand

We study under what conditions massive fields can be "frozen" rather than integrated out in certain four dimensional theories with global or local N=1 supersymmetry.

• We focus on models without gauge fields, admitting a superpotential of the form W = W0(H) + epsilon W1(H,L), with epsilon << 1, where H and L schematically denote the heavy and light chiral superfields.
• We find that the fields H can always be frozen to constant values H0, if they approximately correspond to supersymmetric solutions along the H directions, independently of the form of the Kahler potential K for H and L, provided K is sufficiently regular.
• In supergravity W0 is required to be of order epsilon at the vacuum to ensure a mass hierarchy between H and L.