Physics and Geometry of Brane Vectors*

In the flexible brane world scenario we use the decomposition of higher dimensional gravity and Kaluza-Klein theories to explore the properties of extra vectors. These vectors were components of higher dimensional metric and are massive due to a Higgs effect which makes the Nambu Goldstone bosons become the longitudinal component of the vector fields. We study the masses of these vectors and their couplings to the Standard Model, by using the embedding geometry. In 5D spacetime we found that the geometry of the brane-bulk world, either intrinsic or extrinsic, depend on the extra vector and the 4D graviton only. Connections between the embedding geometry and coset construction by non-linear realization are also discussed.