An Effective Description of the Landscape - II

TL;DR

The paper addresses when heavy fields in 4D ${\cal N}=1$ SUSY theories can be frozen rather than integrated out, expanding previous work to include gauge fields and ${\cal O}(1)$ Yukawas. It develops a manifestly SUSY framework showing that, under conditions like ${\partial_H W_0=0}$ and ${\langle W_0\rangle \sim O(\epsilon)}$, the simple EFT built by freezing heavy fields reliably reproduces the full theory up to controlled corrections ${\cal O}(\epsilon^2)$ in $W$ and ${\cal O}(\epsilon^3)$ in the scalar potential, with SUSY breaking confined to light fields. The analysis extends to chiral+vector multiplets, revealing that heavy vector fields cannot generally be frozen due to gauge invariance, but integrating them out yields a consistent EFT when proper gauge fixing is applied, and the gauge kinetic functions ${f_A}$ and D-terms receive only subleading corrections. The results provide practical criteria for constructing tractable low-energy descriptions from string-inspired SUGRA models with multiple mass hierarchies, including how to handle gauge sectors and potential moduli freezing.

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.