Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions

TL;DR

This paper introduces a gauge-Higgs unification model with spontaneously created fuzzy extra dimensions, specifically a fuzzy torus, which naturally suppresses Higgs mass divergences and addresses the naturalness problem.

Contribution

It presents a novel model where fuzzy extra dimensions emerge spontaneously, providing a new approach to Higgs naturalness and demonstrating divergence suppression.

Findings

Quadratic divergence in Higgs mass is absent at one-loop.

Quantum corrections to Higgs mass are suppressed by symmetries.

Model includes a fuzzy torus as vacuum in gauge theory.

Abstract

We propose gauge-Higgs unification in fuzzy extra dimensions as a possible solution to the Higgs naturalness problem. In our approach, the fuzzy extra dimensions are created spontaneously as a vacuum solution of certain four-dimensional gauge theory. As an example, we construct a model which has a fuzzy torus as its vacuum. The Higgs field in our model is associated with the Wilson loop wrapped on the fuzzy torus. We show that the quadratic divergence in the mass of the Higgs field in the one-loop effective potential is absent. We then argue based on symmetries that the quantum corrections to the Higgs mass is suppressed including all loop contributions. We also consider a realization on the worldvolume theory of D3-branes probing $C^3/(Z_N \times Z_N)$ orbifold with discrete torsion.