Universal Landau Pole

Our understanding of quantum gravity suggests that at the Planck scale the usual geometry loses its meaning. If so, the quest for grand unification in a large non-Abelian group naturally endowed with the property of asymptotic freedom may also lose its motivation. Instead, we propose a unification of all fundamental interactions at the Planck scale in the form of a universal Landau pole, at which all gauge couplings diverge. The Higgs quartic coupling also diverges while the Yukawa couplings vanish. The unification is achieved with the addition of fermions with vector gauge couplings coming in multiplets and with hypercharges identical to those of the standard model. The presence of these particles also prevents the Higgs quartic coupling from becoming negative, thus avoiding the instability (or metastability) of the standard model vacuum.

Figure 1

The running of ${\alpha }_i$, the inverse of the gauge couplings. The dotted lines are the runnings in the absence of quarkons and leptos. The ${\alpha }_i$ are in descending order as $i$ increases.

Figure 2

The running of $y_t$. The dotted line is the SM case.

Figure 3

The running of quartic coupling of the Higgs field. The dotted line shows the instability that the standard model develops in the presence of a Higgs mass of 124–126 GeV.