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Radiative Scherk-Schwarz supersymmetry breaking

We analyze the Scherk-Schwarz (SS) supersymmetry breaking in brane-world five dimensional theories compactified on the orbifold $S^1/\mathbb{Z}_2$. The SS breaking parameter is undetermined at the tree-level (no-scale supergravity) and can be interpreted as the Hosotani vacuum expectation value corresponding to the $U(1)_R$ group in five dimensional N=2 (ungauged) supergravity. We show that the SS breaking parameter is fixed at the loop level to either 0 or 1/2 depending on the matter content propagating in the bulk but in a rather model-independent way. Supersymmetry breaking is therefore fixed through a radiative Scherk-Schwarz mechanism. We also show that the two discrete values of the SS parameter, as well as the supersymmetry breaking shift in the spectrum of the bulk fields, are altered in the presence of a brane-localized supersymmetry breaking arising from some hidden sector dynamics. The interplay between the SS and the brane localized breaking is studied in detail.