General Perturbations for Braneworld Compactifications and the Six Dimensional Case

TL;DR

This paper analyzes how higher codimension braneworld models differ from 5D cases, deriving classical dynamics, studying 6D supergravity compactifications, and revealing stability, spectra, and gauge symmetry features, including effects of negative tension branes.

Contribution

It provides a comprehensive derivation of fluctuation dynamics in higher codimension models and explores the spectra and gauge symmetries in 6D supergravity compactifications, including negative tension branes.

Findings

Complete solution for spectra in unwarped models with positive tension branes.

Identification of extra massless vector fields in negative tension brane models.

Low energy effective theory cannot distinguish between smooth and deformed sphere compactifications.

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.