  Our main objective is to study how braneworld models of higher codimension
differ from the 5D case and traditional Kaluza-Klein compactifications. We
first derive the classical dynamics describing the physical fluctuations in a
wide class of models incorporating gravity, non-Abelian gauge fields, the
dilaton and two-form potential, as well as 3-brane sources. Next, we use these
results to study braneworld compactifications in 6D supergravity, focusing on
the bosonic fields in the minimal model; composed of the supergravity-tensor
multiplet and the U(1) gauge multiplet whose flux supports the
compactification. For unwarped models sourced by positive tension branes, a
harmonic analysis allows us to solve the large, coupled, differential system
completely and obtain the full 4D spin-2,1 and 0 particle spectra, establishing
(marginal) stability and a qualitative behaviour similar to the smooth sphere
compactification. We also find interesting results for models with negative
tension branes; extra massless Kaluza-Klein vector fields can appear in the
spectra, beyond those expected from the isometries in the internal space. These
fields imply an enhanced gauge symmetry in the low energy 4D effective theory
obtained by truncating to the massless sector, which is explicitly broken as
higher modes are excited, until the full 6D symmetries are restored far above
the Kaluza-Klein scale. Remarkably, the low energy effective theory does not
seem to distinguish between a compactification on a smooth sphere and these
singular, deformed spheres.
