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

TL;DR

This paper analyzes the bosonic spectrum and classical stability of a specific type-IIB flux compactification that breaks supersymmetry, identifying boundary conditions that ensure perturbative stability despite complex spectral features.

Contribution

It provides an exact analysis of the bosonic spectra, boundary conditions, and stability criteria for a class of supersymmetry-breaking flux compactifications in type-IIB string theory.

Findings

Zero modes are exactly determined by first-order equations.

Certain boundary conditions lead to perturbative stability.

Stability regions expand as flux-to-interval ratio decreases.

Abstract

We recently constructed type-IIB compactifications to four dimensions depending on a single additional coordinate, where a five-form flux $\Phi$ on an internal torus leads to a constant string coupling. Supersymmetry is fully broken 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 boundary conditions result in the emergence of zero modes, which are determined exactly by first-order equations. The different sectors of the spectrum can be related to Schr\"odinger operators on a finite interval, characterized by pairs of real constants $\mu$ 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 trigonometric ones. With vanishing internal momenta, one can thus identify a wide range of boundary conditions granting perturbative stability, despite the intricacies that emerge in some sectors. For the Kaluza--Klein excitations of non-singlet vectors and scalars the Schr\"odinger systems couple pairs of fields, and the stability regions, which depend on the background, widen as the ratio ${\Phi}/{\ell^4}$ decreases.