We study the quantum stability of type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is broken à la Scherk–Schwarz (SS) by twisting periodicity conditions along a circle of radius R. In particular, we compute the R-dependence of the one-loop induced vacuum energy density ρ(R), or cosmological constant.

For SS twists different from Z₂ we always find, for both orbifolds and orientifolds, a monotonic ρ(R)<0, eventually driving the system to a tachyonic instability. For Z₂ twists, orientifold models can have a different behavior, leading either to a runaway decompactification limit or to a negative minimum at a finite value R₀. The last possibility is obtained for a 4D chiral orientifold model where a more accurate but yet preliminary analysis seems to indicate that R₀→∞ or towards the tachyonic instability, as the dependence on the other geometric moduli is included.