An Effective Description of the Landscape - II

TL;DR

This paper investigates the conditions under which effective theories with frozen massive fields are reliable in four-dimensional N=1 supersymmetric models, including gauge fields and Yukawa interactions, extending previous analyses.

Contribution

It extends prior work by analyzing the reliability of frozen fields in theories with gauge interactions and Yukawa terms, providing criteria for when simple effective theories are valid.

Findings

Heavy chiral fields can be frozen if near supersymmetric solutions and superpotential is small.

In supergravity, a small superpotential at the minimum supports freezing heavy fields.

Frozen effective theories are reliable under specific mass hierarchy and supersymmetry conditions.

Abstract

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 Kaehler 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.