A Solvable Model for Fermion Masses on a Warped 6D World with the Extra 2D Sphere

TL;DR

This paper presents an exactly solvable model for fermion masses in a warped six-dimensional universe with a two-dimensional spherical extra space, offering an alternative to traditional monopole-based models.

Contribution

It introduces a new warp factor solution to the 6D Einstein equations that enables fermion zero modes without relying on Dirac's monopole.

Findings

Provides an explicit warp factor solution $ heta ,\, ext{and}\,\, ext{phi}$

Demonstrates the existence of fermion zero modes in this setup

Offers a novel approach to fermion mass generation in higher-dimensional models

Abstract

In a warped 6D world with an extra 2-dimensional sphere, we propose an exactly solvable model for fermion masses with zero mode. The warp factor is given by $\phi (\theta ,\varphi )=\sin{\theta }\cos{\varphi }$, which is a solution to the 6D Einstein equation with the bulk cosmological constant $\Lambda $ and the energy-momentum tensor of the bulk matter fields. Our model provides another possibility of obtaining fermion zero mode, rather than traditional model based on Dirac's monopole.