Brane Vector Dynamics from Embedding Geometry

TL;DR

This paper investigates the properties and dynamics of extra vectors emerging from higher-dimensional gravity in brane world models, revealing their mass generation mechanism and couplings to Standard Model fields.

Contribution

It provides a detailed analysis of vector fields from embedding geometry, including their mass, couplings, and relation to the coset construction in brane scenarios.

Findings

Vectors acquire mass via a gravitational Higgs mechanism.

Vector mass depends on the radion (dilaton) field's vacuum expectation value.

The embedding geometry determines the vector and graviton structure in 5D models.

Abstract

A Kaluza-Klein decomposition of higher dimensional gravity is performed in the flexible brane world scenario and the properties of the extra vectors resulting from this decomposition are explored. These vectors become massive due to a gravitational Higgs mechanism in which the brane oscillation Nambu-Goldstone bosons become the longitudinal component of the vector fields. The vector mass is found to be proportional to the exponential of the vacuum expectation value of the radion (dilaton) field and as such its magnitude is model dependent. Using the structure of the embedding geometry, the couplings of these vectors to the Standard Model, including those resulting from the extrinsic curvature, are deduced. As an example, we show that for 5D space-time the geometry of the bulk-brane world, either intrinsic or extrinsic, only depends on the extra vector and the 4D graviton. The connection between the embedding geometry and coset construction by non-linear realization is also presented.