Globally and locally supersymmetric effective theories for light fields

TL;DR

This paper develops a systematic method to derive low-energy effective theories in supersymmetric models, ensuring they remain approximately supersymmetric when integrating out heavy fields, applicable to both global and local supersymmetry including gravity.

Contribution

It introduces a simple, algebraic prescription for integrating out heavy superfields in a way that preserves supersymmetry and applies universally to global and local theories with matter and gravity.

Findings

Conditions for approximate supersymmetry in low-energy theories identified.

A universal prescription for integrating out heavy superfields established.

The method preserves supersymmetry and commutes with gravity inclusion.

Abstract

We reconsider the general question of how to characterize most efficiently the low-energy effective theory obtained by integrating out heavy modes in globally and locally supersymmetric theories. We consider theories with chiral and vector multiplets and identify the conditions under which an approximately supersymmetric low-energy effective theory can exist. These conditions translate into the requirements that all the derivatives, fermions and auxiliary fields should be small in units of the heavy mass scale. They apply not only to the matter sector, but also to the gravitational one if present, and imply in that case that the gravitino mass should be small. We then show how to determine the unique exactly supersymmetric theory that approximates this effective theory at the lowest order in the counting of derivatives, fermions and auxiliary fields, by working both at the superfield level and with component fields. As a result we give a simple prescription for integrating out heavy superfields in an algebraic and manifestly supersymmetric way, which turns out to hold in the same form both for globally and locally supersymmetric theories, meaning that the process of integrating out heavy modes commutes with the process of switching on gravity. More precisely, for heavy chiral and vector multiplets one has to impose respectively stationarity of the superpotential and the Kahler potential.