Runaway directions in O'Raifeartaigh models

TL;DR

This paper investigates the conditions under which runaway directions occur in O'Raifeartaigh models due to R-symmetries and non-R symmetries, clarifying previous issues and providing a generic model example.

Contribution

It refines the understanding of runaway directions in O'Raifeartaigh models, clarifies fractional charge and genericness issues, and introduces a generic anomaly-free model illustrating non-R symmetry related runaways.

Findings

Runaway directions are linked to both R-symmetries and non-R symmetries.

A refined set of conditions for the occurrence of runaway directions.

Existence of a generic, anomaly-free model demonstrating non-R symmetry runaways.

Abstract

R-symmetries, which are needed for supersymmetry (SUSY) breaking in O'Raifeartaigh models, often lead to SUSY runaway directions trough a complexified R-transformation. Non-R symmetries also lead to runaway directions in a similar way. This work investigates the occurrence of runaway directions of both SUSY and SUSY breaking types. We clarify previous issues on fractional charges and genericness, and make a refined statement on conditions for runaway directions related to either R-symmetries or non-R symmetries. We present a generic and anomaly-free model to show the existence of runaway directions related to non-R symmetries. We also comment on the possibility to combine the non-R symmetry case to the R-symmetry case by an R-charge redefinition.