For SU(2) with 24 and 48 Dirac flavors, the lattice gradient-flow coupling matches the perturbative two-loop running at accessible scales and refuses to grow large, which is compatible with a Landau pole but does not disprove a strong-coupling ultraviolet fixed point.
Asymptotically Safe Standard Model Extensions?
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abstract
We consider theories with a large number $N_F$ of charged fermions and compute the renormalisation group equations for the gauge, Yukawa and quartic couplings resummed at leading order in $1/N_F$. We construct extensions of the Standard Model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.
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Safety versus triviality on the lattice
For SU(2) with 24 and 48 Dirac flavors, the lattice gradient-flow coupling matches the perturbative two-loop running at accessible scales and refuses to grow large, which is compatible with a Landau pole but does not disprove a strong-coupling ultraviolet fixed point.