On string models with Scherk-Schwarz supersymmetry breaking

We construct a general class of chiral four-dimensional string models with Scherk--Schwarz supersymmetry breaking, involving freely acting orbifolds. The basic ingredient is to combine an ordinary supersymmetry-preserving Z_N projection with a supersymmetry-breaking projection Z_M' acting freely on a subspace of the internal manifold. A crucial condition is that any generator of the full orbifold group Z_N x Z_M' must either preserve some supersymmetry or act freely in order to become irrelevant in some large volume limit. Tachyons are found to be absent or limited to a given region of the tree-level moduli space. We find several new models with orthogonal supersymmetries preserved at distinct fixed-points. Particular attention is devoted to an interesting Z_3 x Z_3' heterotic example.