Massive $U(1)$ gauge field and their accompanying scalars in brane world

TL;DR

This paper investigates the effects of adding a specific term to the bulk U(1) gauge field action in brane-world models, revealing new scalar mode behaviors and mass hierarchies on different brane dimensions.

Contribution

It introduces a term bla^M X_M)^2 into the bulk gauge action, breaking full gauge invariance but maintaining residual symmetry, and analyzes resulting scalar mode properties.

Findings

Scalar KK modes are lighter than vector KK modes on 5D branes.

Two types of scalar modes appear on 6D branes with oscillating interactions.

The modified action affects the mass spectrum and mode dynamics in brane-world scenarios.

Abstract

In brane-world scenarios, the effective action of a massless bulk \(U(1)\) gauge field preserves gauge invariance via couplings between massive vector Kaluza-Klein (KK) modes and scalar KK modes. In this work, we extend this framework by introducing a term \((\nabla^M X_M)^2\) into the massless bulk \(U(1)\) gauge action. This modification explicitly breaks the full gauge redundancy while preserving a residual gauge symmetry both in the bulk and on the brane. In this setup, the scalar KK modes can acquire masses from the background geometry. Notably, we find that on the 5D brane, these scalar KK modes are lighter than the vector KK modes. In contrast, on the 6D brane, two types of scalar modes emerge; the mixed interactions between them give rise to oscillations among these scalar modes.