R-symmetry, supersymmetry breaking and metastable vacua in global and local supersymmetric theories

TL;DR

This paper investigates how explicit R-symmetry breaking affects supersymmetry breaking and metastability in N=1 supersymmetric theories, providing classifications and examples within global and local frameworks.

Contribution

It classifies R-symmetry breaking terms and analyzes their impact on SUSY vacua, including conditions for metastability and exceptions to known theorems.

Findings

R-breaking terms can lead to metastable SUSY breaking vacua.

Certain R-breaking terms do not produce SUSY solutions, especially in supergravity.

The Nelson-Seiberg theorem generally holds in local SUSY, with specific exceptions.

Abstract

We study N=1 global and local supersymmetric theories with a continuous global $U(1)_R$ symmetry as models of dynamical supersymmetry (SUSY) breaking. We introduce explicit R-symmetry breaking terms into such models, in particular a generalized O'Raifeartaigh model. Such explicit R-symmetry breaking terms can lead to a SUSY preserving minimum. We classify explicit R-symmetry breaking terms by the structure of newly appeared SUSY stationary points as a consequence of the R-breaking effect, which could make the SUSY breaking vacuum metastable. We show that the R-breaking terms are basically divided into two categories. One of them does not generate a SUSY solution, or yields SUSY solutions that disappear in the case of supergravity when we tune a parameter so that the original SUSY breaking minimum becomes a Minkowski vacuum. We also show that the general argument by Nelson and Seiberg for a dynamical SUSY breaking still holds with a local SUSY except for a certain nontrivial case, and present concrete examples of the exception.