Six Dimensional Gauge-Higgs Unification with an Extra Space S^2 and the Hierarchy Problem

TL;DR

This paper investigates the quantum corrections to the Higgs mass in a six-dimensional gauge theory compactified on a two-sphere, proposing a natural solution to the hierarchy problem through finiteness and vanishing of the Higgs mass.

Contribution

It demonstrates that the one-loop radiative correction to the Higgs mass in this model is finite and vanishes for small bulk scalar mass, offering insights into gauge-Higgs unification and hierarchy problem.

Findings

Radiative Higgs mass correction is finite for arbitrary bulk scalar mass.

The correction vanishes for small scalar mass, suggesting a natural solution to the hierarchy problem.

Kaluza-Klein modes exhibit a Higgs-like mechanism and supersymmetry features.

Abstract

We calculate one-loop radiative correction to the mass of Higgs identified with the extra space components of the gauge field in a six dimensional massive scalar QED compactified on a two-sphere. The radiatively induced Higgs mass is explicitly shown to be finite for arbitrary bulk scalar mass M. Furthermore, the remaining finite part also turns out to vanish, at least for the case of small M, thus suggesting that the radiatively induced Higgs mass exactly vanishes, in general. The non-zero "Kaluza-Klein" modes in the gauge sector are argued to have a Higgs-like mechanism and quantum mechanical N=2 supersymmetry, while the Higgs zero modes, as supersymmetric states, have a close relation with monopole configuration.