Abstract
Abstract
We recently constructed type-IIB compactifications to four dimensions depending on a single additional coordinate, where a five-form flux Φ on an internal torus leads to a constant string coupling. Supersymmetry is fully broken when the internal manifold includes a finite interval of length ℓ, which is spanned by a conformal coordinate in a finite range 0 < z < zm. 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 Schrödinger operators on a finite interval, characterized by pairs of real constants μ and $$ \overset{\sim }{\mu } $$
μ
~
, with μ equal to 1/3 or 2/3 in all cases and different values of $$ \overset{\sim }{\mu } $$
μ
~
. The potentials behave as $$ \frac{\mu^2-1/4}{z^2} $$
μ
2
−
1
/
4
z
2
and $$ \frac{{\overset{\sim }{\mu}}^2-1/4}{{\left({z}_m-z\right)}^2} $$
μ
~
2
−
1
/
4
z
m
−
z
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 Schrödinger systems couple pairs of fields, and the stability regions, which depend on the background, widen as the ratio Φ/ℓ4 decreases.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
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