Scalar mode analysis of the warped Salam-Sezgin model

We study the scalar perturbation sector of the general axisymmetric warped Salam-Sezgin model with codimension-2 branes. We focus on the perturbations which mix with the dilaton. We show that the scalar fluctuation analysis can be reduced to studying two scalar modes of constant wavefunction, plus modes of non-constant wavefunction which obey a single Schrödinger equation. From the obtained explicit solution of the scalar modes, we point out the importance of the non-constant modes in describing the four-dimensional effective theory. This observation remains true for the unwarped case and was neglected in the relevant literature. Furthermore, we show that due to these modes, the warped solutions can be unstable for a certain region of the parameter space.