Five benefits of grand unified $SU(5)$ brane world scenario

TL;DR

This paper constructs a five-dimensional grand unified $SU(5)$ brane-world model that localizes Standard Model particles and solves key issues like doublet-triplet splitting using scalar fields and geometric mechanisms.

Contribution

It introduces a novel, economical five-dimensional $SU(5)$ GUT model with localized fermions, gauge fields, and Higgs, achieving symmetry breaking and doublet-triplet splitting.

Findings

Successfully localizes chiral fermions and gauge fields on the brane.

Realizes $SU(5)$ breaking down to the Standard Model gauge group.

Reproduces Standard Model Yukawa couplings via RG analysis.

Abstract

We construct an $SU(5)$ Grand Unified Theory on domain walls in the five-dimensional space-time. In this setup, we introduce an adjoint scalar field and a singlet that together form a set of five domain-wall solutions, realizing a dynamical brane-world. The same scalar fields also localize chiral fermion zero modes around the walls via the Jackiw-Rebbi mechanism, break $SU(5)$ down to the Standard Model gauge group via geometric Higgs mechanism and simultaneously trap gauge fields through a field-dependent gauge kinetic term. Furthermore, they enable localization of the Higgs field, providing a novel solution to the doublet-triplet splitting problem. As a result, all essential ingredients of the model are realized by a single adjoint scalar field and a singlet, making the construction very economical. We propose two realizations of the Higgs sector, derive the four-dimensional effective theory, and demonstrate that the Standard Model Yukawa couplings at the weak scale can be reproduced from the five-dimensional Yukawa couplings by the renormalization group analysis with a suitable choice of parameters.