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.
Chronological Inversion Method for the Dirac Matrix in Hybrid Monte Carlo
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abstract
In Hybrid Monte Carlo simulations for full QCD, the gauge fields evolve smoothly as a function of Molecular Dynamics time. Here we investigate improved methods of estimating the trial or starting solutions for the Dirac matrix inversion as superpositions of a chronological sequence of solutions in the recent past. By taking as the trial solution the vector which minimizes the residual in the linear space spanned by the past solutions, the number of conjugate gradient iterations per unit MD time is decreased by at least a factor of 2. Extensions of this basic approach to precondition the conjugate gradient iterations are also discussed.
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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.