Extra Spacetime Dimensions and Unification

TL;DR

The paper investigates how large-radius extra spacetime dimensions, appearing at an intermediate scale, modify the running of gauge and Yukawa couplings in the MSSM. Using a nonrenormalizable effective theory with KK towers for gauge and Higgs fields (no fermion KK modes), it shows that gauge coupling unification can persist at a lower, perturbative scale, while Yukawa couplings receive finite power-law corrections that can reduce or even erase fermion mass hierarchies. It also discusses proton-decay constraints and proposes KK selection rules as a mechanism to suppress or cancel proton decay, and outlines how Yukawa unification can align with gauge unification. The work points to rich phenomenology, including possible explicit models, connections to string theory, and potential gauge–gravity unification, with or without supersymmetry.

Abstract

We study the effects of extra spacetime dimensions at intermediate mass scales, as expected in string theories with large-radius compactifications, and focus on the gauge and Yukawa couplings within the Minimal Supersymmetric Standard Model. We find that extra spacetime dimensions naturally lead to the appearance of grand unified theories at scales substantially below the usual GUT scale. Furthermore, we show that extra spacetime dimensions provide a natural mechanism for explaining the fermion mass hierarchy by permitting the Yukawa couplings to receive power-law corrections. We also discuss how proton-decay constraints may be addressed in this scenario, and suggest that proton-decay amplitudes may be exactly cancelled to all orders in perturbation theory as a result of new Kaluza-Klein selection rules corresponding to the extra spacetime dimensions.

Figures (3)

• Figure 1: Unification of gauge couplings in the presence of extra spacetime dimensions. We consider four representative cases: $\mu_0 = 10^{5}$ GeV (top left), $\mu_0 = 10^{8}$ GeV (top right), $\mu_0 = 10^{11}$ GeV (bottom left), and $\mu_0 = 10^{15}$ GeV (bottom right). In each case we have taken $\delta=1$.
• Figure 2: The unified coupling $(\alpha'_{\rm GUT})^{-1}$ as a function of the unification scale $M'_{\rm GUT}$. This curve is independent of the number of extra spacetime dimensions. The limit of the usual four-dimensional MSSM is indicated with a dot.
• Figure 3: The evolution of the Yukawa couplings $\alpha_F^{-1}\equiv 4\pi / y_F^2$ within the MSSM, assuming the presence of a single extra dimension at $\mu_0=10^{8}$ GeV. We have taken $m_t=180$ GeV and $\tan\beta=3$ as a representative case. Note that we are plotting the Yukawa couplings on a logarithmic scale in order to display them all simultaneously. It is evident that all of the Yukawa couplings approach a common Landau pole which precisely agrees with the scale at which the gauge couplings unify.