Supersymmetry in non-simply-connected space-time

Supersymmetric and similar models were studied in flat space-time with the topology of R3xS1. In the former model two cases were studied: in one case a critical length was found below which supersymmetry is spontaneously broken and in the other case a critical length was found at which softly broken supersymmetry is restored and below the critical length it is again broken. In the latter model, twisted fields are included and it is shown that under certain conditions this inclusion can make the tree vacuum unstable. In the limit of exact supersymmetry, the topological mass generated vanishes identically implying that supersymmetry is left unbroken by radiative corrections (at the one-loop-level) if it is so at the tree level. The results are derived through a study of the one-loop effective potential for the scalar field. (author)