# Realization of a spontaneous gauge and supersymmetry breaking vacuum

## TL;DR

This paper explores a model where gauge symmetry and supersymmetry are simultaneously broken in a stable vacuum, with loop effects lifting flat directions and spontaneous R-symmetry breaking, applicable to grand unified theories.

## Contribution

It introduces a mechanism for breaking gauge symmetry and SUSY together, with loop effects stabilizing the vacuum and spontaneous R-symmetry breaking, extending to non-Abelian gauge theories.

## Key findings

- Gauge and SUSY breaking occur simultaneously in the model.
- Loop effects lift flat directions, stabilizing the vacuum.
- Gaugino masses are generated by R-symmetry breaking.

## Abstract

It is one of the major issues to realize a vacuum which breaks supersymmetry (SUSY) and R-symmetry, in a supersymmetric model. We study the model, where the same sector breaks the gauge symmetry and SUSY. In general, the SUSY breaking model without gauge symmetry has a flat direction at the minimum of F-term scalar potential. When we introduce U(1) gauge symmetry to such a SUSY breaking model, there can appear a runaway direction. Such a runway direction can be lifted by loop effects, and the gauge symmetry breaking and SUSY breaking are realized. The R-symmetry, that is assigned to break SUSY, is also spontaneously broken at the vacuum. This scenario can be extended to non-Abelian gauge theories. We also discuss application to the Pati-Salam model and the SU(5) grand unified theory. We see that non-vanishing gaugino masses are radiatively generated by the R-symmetry breaking and the gauge messenger contribution.