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.
Directions for model building from asymptotic safety
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abstract
Building on recent advances in the understanding of gauge-Yukawa theories we explore possibilities to UV-complete the Standard Model in an asymptotically safe manner. Minimal extensions are based on a large flavor sector of additional fermions coupled to a scalar singlet matrix field. We find that asymptotic safety requires fermions in higher representations of $SU(3)_C\times SU(2)_L$. Possible signatures at colliders are worked out and include $R$-hadron searches, diboson signatures and the evolution of the strong and weak coupling constants.
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hep-lat 1years
2019 1verdicts
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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.