On the quantum stability of type IIB orbifolds and orientifolds with Scherk–Schwarz SUSY breaking

We study the quantum stability of type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is broken a 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.