Supersymmetry Breaking through Boundary Conditions Associated with the $U(1)_{R}$

TL;DR

This paper explores how boundary conditions in compactified supersymmetric theories, especially involving $U(1)_R$ transformations, can induce universal soft supersymmetry breaking terms, analyzed through toy models like supersymmetric QED and QCD.

Contribution

It introduces a novel mechanism for supersymmetry breaking via boundary conditions associated with $U(1)_R$ transformations in compactified spaces.

Findings

Boundary conditions can break supersymmetry and generate soft terms.

Toy models demonstrate the mechanism's effects on supersymmetric QED and QCD.

Universal soft supersymmetry breaking terms are achievable through boundary conditions.

Abstract

The effects of boundary conditions of the fields for the compactified space directions on the supersymmetric theories are discussed. The boundary conditions can be taken to be periodic up to the degrees of freedom of localized $U(1)_{R}$ transformations. The boundary condition breaks the supersymmery to yield universal soft supersymmetry breaking terms. The 4-dimensional supersymmetric QED with one flavour and the pure supersymmetric QCD are studied as toy models when one of the space coordinates is compactified on $S^1$.