An Effective Description of the Landscape - I

TL;DR

This paper investigates conditions under which heavy fields in supersymmetric theories can be fixed at constant values without significant backreaction, simplifying the analysis of moduli stabilization in string-inspired models.

Contribution

It provides criteria for freezing heavy fields in N=1 supersymmetric models, showing this is valid under broad conditions and justifies common stabilization methods.

Findings

Heavy fields can be frozen at supersymmetric solutions independently of the Kahler potential.

Backreaction from supersymmetry breaking on heavy fields is negligible, leading to suppressed F-terms.

The results support the reliability of moduli stabilization techniques used in string compactifications.

Abstract

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. The backreaction induced by the breaking of supersymmetry on the heavy fields is always negligible, leading to suppressed F^H--terms. For factorizable Kahler potentials W0 can instead be generic. Our results imply that the common way complex structure and dilaton moduli are stabilized, as in Phys. Rev. D 68 (2003) 046005 by Kachru et al., for instance, is reliable to a very good accuracy, provided W0 is small enough.