The Gauge Hierarchy Problem and Higher Dimensional Gauge Theories

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.

Figures (3)

• Figure 1: The $m_{H}^2$ measured in the unit of $e^{2}/(2\sqrt{2}\pi^2L^2)$ as a function of $mL$ in the case of periodic b.c..
• Figure 2: The 3D plot of $m_{H}^2$ (in the unit of $e^{2}/(2\sqrt{2}\pi^2L^2)$) as a function of $a$ and $mL$, with $a$ standing for $\alpha$.
• Figure 3: The vacuum energy density $V$ in the unit of $\frac{1}{2\sqrt{2} \pi^2 L^4}$ as a function of $a$, with $a$ standing for $\alpha = e A_y^c L$.