Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions

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.

1+38 pages, 4 figures v2: refs added

References in corpus (7)

• Non-perturbative effects on seven-brane Yukawa couplings
• Yukawa Couplings in F-theory and Non-Commutative Geometry
• Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
• Evidence for F(uzz) Theory
• Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• D-branes Wrapped on Fuzzy del Pezzo Surfaces

Cited by in corpus (3)

• Spinning squashed extra dimensions and chiral gauge theory from $\mathcal{N}=4$ SYM
• Large Field Excursions from Dimensional (De)construction
• Extra-Natural Inflation (De)constructed