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We recently constructed type-IIB compactifications to four dimensionsdepending on a single additional coordinate, where a five-form flux $\Phi$ onan internal torus leads to a constant string coupling. Supersymmetry is fullybroken when the internal manifold includes a finite interval of length $\ell$,which is spanned by a conformal coordinate in a finite range $0 < z < z_m$.Here we examine the low-lying bosonic spectra and their classical stability,paying special attention to self-adjoint boundary conditions. Special boundaryconditions result in the emergence of zero modes, which are determined exactlyby first-order equations. The different sectors of the spectrum can be relatedto Schr\"odinger operators on a finite interval, characterized by pairs of realconstants $\mu$ and $\tilde{\mu}$, with $\mu$ equal to ${1}/{3}$ or ${2}/{3}$in all cases and different values of $\tilde{\mu}$. The potentials behave as$\frac{\mu^2-1/4}{z^2}$ and $\frac{\tilde{\mu}^2-1/4}{\left(z_m-z\right)^2}$near the ends and can be closely approximated by exactly solvable trigonometricones. With vanishing internal momenta, one can thus identify a wide range ofboundary conditions granting perturbative stability, despite the intricaciesthat emerge in some sectors. For the Kaluza--Klein excitations of non-singletvectors and scalars the Schr\"odinger systems couple pairs of fields, and thestability regions, which depend on the background, widen as the ratio${\Phi}/{\ell^4}$ decreases.

A 4D IIB Flux Vacuum and Supersymmetry Breaking. II. Bosonic Spectrum and Stability