Gauge Coupling Unification with Extra Dimensions and Gravitational Scale Effects

Abstract

We study gauge coupling unification in the presence of extra dimensions compactified at a few TeV. Achieving unification requires a large number of gauge boson Kaluza-Klein excitations lighter than the string scale, such that the higher-dimensional gauge couplings are O(1) in string scale units. Corrections to the gauge couplings from two or more loops are about 10% or larger, hence string (or M) theory is generally expected to be strongly coupled in TeV-scale extra-dimensional scenarios. Higher-dimensional operators induced by quantum gravitational effects can shift the gauge couplings by a few percent. These effects are sufficiently large that even the minimal Standard Model, or the MSSM, allow unification at a scale in the TeV range. The strongly coupled unified theory may induce dynamical electroweak symmetry breaking.

Figures (3)

• Figure 1: Loop contribution of the operator (\ref{['phiphi']}), represented by the blob, to the gauge kinetic term.
• Figure 2: Running of the SM gauge couplings for a) $\delta=1$, and b) $\delta=2$ extra dimensions. Solid curves are the 1-loop results in the continuous limit. The dashed curves include the two-loop contributions from the KK states, assuming $\xi=1$ in Eq. (\ref{['RGE']}). The KK excitations of the gauge bosons do not affect $\alpha_1^{-1}$ directly because the gauge group is Abelian. The compactification scale is assumed to be $1/R=3$ TeV.
• Figure 3: The percentage corrections of $\alpha_2^{-1}$ and $\alpha_3^{-1}$in the Standard Model due to the 2-loop effects, $\sigma_i = (\alpha_{i,\,{\rm 2-loop}}^{-1}/ \alpha_{i,\,{\rm 1-loop}}^{-1})(\mu)-1$, with $\xi=0.5$ (solid lines) and $\xi=1$ (dashed lines), for: a) $\delta =1$, and b) $\delta =2$.