Grand Unification in Higher Dimensions

TL;DR

The paper presents a higher-dimensional grand unified theory in which a bulk gauge group G is broken to the Standard Model on lower-dimensional defects, enabling gauge coupling unification and quark–lepton quantum numbers to arise from the symmetrical bulk while Higgs and flavor features originate at the defects. This setup yields high predictivity when the theory remains valid up to a strong coupling scale, including a precise prediction for $\sin^2\theta_W$ and explicit scales $M_c$ and $M_s$, with proton decay dominated by dimension-6 X-boson exchange. The minimal 5D SU(5) model with a single 3-2-1 defect gives $M_c \approx 5\times 10^{14}$ GeV and $M_s \approx 1\times 10^{17}$ GeV, and the predicted flavor structure naturally accommodates large neutrino mixing while suppressing dangerous dimension-5 proton-decay operators via an $R$ symmetry. If supersymmetry breaking is realized via boundary misalignment, the framework predicts a calculable superpartner spectrum and sizeable lepton-flavor violation, providing concrete experimental tests of the geometric unification approach.

Abstract

We have recently proposed an alternative picture for the physics at the scale of gauge coupling unification, where the unified symmetry is realized in higher dimensions but is broken locally by a symmetry breaking defect. Gauge coupling unification, the quantum numbers of quarks and leptons and the longevity of the proton arise as phenomena of the symmetrical bulk, while the lightness of the Higgs doublets and the masses of the light quarks and leptons probe the symmetry breaking defect. Moreover, the framework is extremely predictive if the effective higher dimensional theory is valid over a large energy interval up to the scale of strong coupling. Precise agreement with experiments is obtained in the simplest theory --- SU(5) in five dimensions with two Higgs multiplets propagating in the bulk. The weak mixing angle is predicted to be sin^2theta_w = 0.2313 \pm 0.0004, which fits the data with extraordinary accuracy. The compactification scale and the strong coupling scale are determined to be M_c \simeq 5 x 10^{14} GeV and M_s \simeq 1 x 10^{17} GeV, respectively. Proton decay with a lifetime of order 10^{34} years is expected with a variety of final states such as e^+pi^0, and several aspects of flavor, including large neutrino mixing angles, are understood by the geometrical locations of the matter fields. When combined with a particular supersymmetry breaking mechanism, the theory predicts large lepton flavor violating mu -> e and tau -> mu transitions, with all superpartner masses determined by only two free parameters. The predicted value of the bottom quark mass from Yukawa unification agrees well with the data. This paper is mainly a review of the work presented in hep-ph/0103125, hep-ph/0111068 and hep-ph/0205067.

Figures (15)

• Figure 1: The predictions for $\alpha_s(M_Z)$ in non-supersymmetric grand unification, $\alpha_s^{\rm GUT}$, and supersymmetric grand unification, $\alpha_s^{\rm SGUT}$. The solid error bar represents the threshold corrections from the superpartner spectrum. Dotted error bars represent threshold corrections from the unified scale corresponding to a heavy ${\bf 5} + \bar{\bf 5}$ representation with unit logarithmic mass splitting between doublets and triplets.
• Figure 2: Physics at high energies probes extra dimensions, $y$, that extend over small sizes $R$. The interactions in the volume of this higher dimensional box are constrained by a unified gauge symmetry $G$, but interactions on a boundary may be constrained only by a smaller symmetry, such as 3-2-1, creating a defect of lower dimension.
• Figure 3: An example of a 3D bulk with a 1D defect.
• Figure 4: In the fifth dimension, space is a line segment with boundaries at $y=0$ and at $y=\pi R$. Solid and dotted lines represent the profiles of gauge transformation parameters $\xi_{321}$ and $\xi_X$, respectively. Because $\xi_X(y = \pi R) = 0$, a point defect occurs in the symmetry at the $y = \pi R$ boundary, explicitly breaking $SU(5)$ to $SU(3)_C \times SU(2)_L \times U(1)_Y$.
• Figure 5: A bulk, having boundary conditions leading to a defect, can be viewed as a "machine" for creating a mass spectrum of 4D particles, known as a KK tower.