Inverse and Dynamical Supersymmetry Breaking in $S^1\times R^3$

TL;DR

This paper investigates how the size of a compact dimension influences supersymmetry breaking in a supersymmetric model, revealing phenomena akin to finite temperature effects and metastable vacua.

Contribution

It demonstrates the conditions under which supersymmetry is dynamically broken or preserved depending on the compactification radius in a specific supersymmetric setup.

Findings

Supersymmetry remains unbroken at small radius for certain interactions.

Supersymmetry breaks dynamically as the radius increases for some interaction terms.

The phenomena resemble finite temperature phase transitions and metastable vacua behaviors.

Abstract

In this paper we study the influence of hard supersymmetry breaking terms in a N=1, $d=4$ supersymmetric model, in $S^1\times R^3$ spacetime topology. It is found that for some interaction terms and for certain values of the couplings, supersymmetry is unbroken for small lengths of the compact radius, and breaks dynamically as the radius increases. Also for another class of interaction terms, when the radius is large supersymmetry is unbroken and breaks dynamically as the radius decreases. It is pointed out that the two phenomena have similarities with the theory of metastable vacua at finite temperature and with the inverse symmetry breaking of continuous symmetries at finite temperature (where the role of the temperature is played by the compact dimension's radius).