# Non-Abelian Gauge Field Localization on Walls and Geometric Higgs Mechanism

## TL;DR

This paper explores a geometric Higgs mechanism in a five-dimensional $SU(N)$ gauge theory with domain walls, analyzing gauge symmetry breaking, mass spectra, and effective theories, with parallels to D-branes in string theory.

## Contribution

It introduces a novel geometric Higgs mechanism via domain wall splitting in a 5D $SU(N)$ gauge theory and derives the low-energy effective theory including non-linear interactions.

## Key findings

- Mass spectra for $SU(5) o SU(3) imes SU(2) imes U(1)$ are detailed.
- A low-energy effective theory with two-derivative interactions is derived.
- Similarities between domain walls and D-branes are observed.

## Abstract

Combining the semi-classical localization mechanism for gauge fields with $N$ domain wall background in a simple $SU(N)$ gauge theory in five space-time dimensions we investigate the geometric Higgs mechanism, where a spontaneous breakdown of the gauge symmetry comes from splitting of domain walls. The mass spectra are investigated in detail for the phenomenologically interesting case $SU(5) \to SU(3)\times SU(2)\times U(1)$ which is realized on a split configuration of coincident triplet and doublet of domain walls. We derive a low energy effective theory in a generic background using the moduli approximation, where all non-linear interactions between effective fields are captured up to two derivatives. We observe novel similarities between domain walls in our model and D-branes in superstring theories.