Abstract
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.
Highlights
Almost two decades on, branes are evermore ubiquitous in the models constructed to understand particle physics and cosmology, with all their How?’s and Why?’s
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
All our bosonic massless modes do fall into well-defined SU(2) representations, and we argue that the classical low energy 4D effective field theory — obtained by truncating to the massless sector — does enjoy an enhanced KK gauge symmetry beyond the isometries! it appears that the low energy theory does not distinguish between compactifications on the smooth sphere and these singular, deformed spheres
Summary
Branes are evermore ubiquitous in the models constructed to understand particle physics and cosmology, with all their How?’s and Why?’s. The first part of this paper can be considered as a generalization of that work, where we include the presence of thin source 3-branes and extra bulk fields that are generically present in supergravity theories; the dilaton and anti-symmetric two-form potential. The spin-1 and spin-0 sectors present large coupled differential systems, and by finding a set of harmonics on the 2D internal space ( the “rugbyball”), we are able to solve these systems analytically for the unwarped case In this way, we obtain all the 4D modes for unwarped compactifications with positive tension brane sources, and. All our bosonic massless modes do fall into well-defined SU(2) representations, and we argue that the classical low energy 4D effective field theory — obtained by truncating to the massless sector — does enjoy an enhanced KK gauge symmetry beyond the isometries!
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