Six-Dimensional Gauge-Higgs Unification with an Extra SpaceS²and the Hierarchy Problem

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.

Lattice gauge theory approach to spontaneous symmetry breaking from an extra dimension

“…(3.13). Then we build the matrix correlation function 19) and write the spectral decompositions Here m, n = 0, 1, 2, ... label the eigenstates |m with energy eigenvalue E m of the Hamiltonian H and T is the temporal size of the lattice. We use the same symbol O i to denote the Euclidean field and the corresponding operator in the Hamiltonian formulation.…”

“…There is no doubt that supersymmetry is an elegant solution to the problem but it could happen that it is not realized at energies accessible in near future collider experiments so it is useful to be aware of alternative solutions. Back then to extra dimensions, in the case where the extra (fifth here) dimension is compactified on a circle, one can carry out a one-loop calculation of the Higgs mass and verify its aforementioned finiteness [11,12] and can even give all order arguments to that effect [13,14,15,16,17,18,19,20], but the problem with this solution is that a simple circle compactification can not be realistic for various reasons, the absence of chiral fermions being one of the main.…”

Fermion dark matter in gauge-Higgs unification

“…An essential property of the GHU scenario is that the SM Higgs doublet is identified with an extra spatial component of the gauge field in higher dimensions. Associated with the higher-dimensional gauge symmetry, the GHU scenario predicts various finite physical observables, irrespective of the non-renormalizability of the scenario, such as the effective Higgs potential [7][8][9][10][11][12], the effective Higgs coupling with digluon/diphoton [13][14][15], the anomalous magnetic moment g − 2 [16,17], and the electric dipole moment [18].…”

Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions

“…Other related recent work discussing the implications of the higher-dimensional point of view on symmetry breaking and Higgs masses can be found in [83,84,85,86]. These issues could now be discussed within a renormalizable framework.…”