The Gauge Hierarchy Problem and Higher Dimensional Gauge Theories

TL;DR

This paper explores how higher dimensional gauge theories can naturally address the gauge hierarchy problem by eliminating divergent mass corrections and analyzing boundary conditions.

Contribution

It demonstrates that in higher dimensional gauge theories, both classical and quantum mass corrections can vanish, offering a potential solution to the hierarchy problem.

Findings

Classical Higgs mass and quantum divergences vanish in higher dimensions.

Finite mass corrections depend on boundary conditions for matter fields.

On the space S^2, even finite mass corrections vanish.

Abstract

We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space $S^2$ even the finite mass correction vanishes.