Discrete Symmetries/Discrete Theories

TL;DR

This paper discusses the constraints and challenges in constructing models of metastable supersymmetry breaking, especially within retrofitted O'Raifeartaigh models, highlighting issues with symmetry breaking and messenger scales.

Contribution

It provides a detailed analysis of the limitations and fine-tuning problems in gauge-mediated and gravity-mediated supersymmetry breaking models.

Findings

Gauge-mediated models require small or finely tuned couplings.

Gravity-mediated models face discrete tuning issues for the gravitino mass.

Model building constraints suggest a natural explanation for the little hierarchy problem.

Abstract

Dynamical, metastable supersymmetry breaking appears to be a generic phenomena in supersymmetric field theories. It's simplest implementation is within the so-called "retrofitted O'Raifeartaigh Models". While seemingly flexible, model building in these theories is significantly constrained. In gauge-mediated versions, if the approximate $R$ symmetry of the theory is spontaneously broken, the messenger scale is fixed; if explicitly broken by retrofitted couplings, a very small dimensionless number is required; if supergravity corrections are responsible for the symmetry breaking, at least two moderately small couplings are required, and there is a large range of possible messenger scales. In gravity mediated versions, achieving $m_{3/2} \approx M_Z$ is a problem of discrete tuning. With plausible assumptions, one can't achieve this to better than a factor of 100, perhaps accounting for a {\it little hierarchy} and the surprisingly large value of the Higgs mass.