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

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).

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