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The running of the bare coupling in SU(N) gauge theories

Presenter: Michael Teper — University of Oxford

Chris Allton, Michael Teper, Aurora Trivini

Interpreting the way that the SU(3) lattice bare coupling runs with the lattice spacing is complicated by the fact that there is a smooth cross-over region in which the strong coupling expansion transforms into a weak-coupling one. For N≥ 5, however, there is a first order bulk transition that cleanly separates the strong and weak coupling regimes. We find that in this case the calculated string tension can be readily fitted throughout the weak coupling region by a standard 3-loop expression modified by lattice spacing corrections of the expected form. While our fits demand the presence of the latter, they do not constrain the perturbative coupling scheme enough to enable us to extract a usefully accurate value of a(β) in units of ΛMS. To help resolve this ambiguity we show that in SU(3) the Parisi mean-field improved coupling scheme closely reproduces results obtained with the Schrodinger Functional coupling scheme both for r0ΛSF and, over a much larger range of β, with no reference to a calculated physical quantity. Using the Parisi scheme we find ΛMS/√σ = 0.503(2)(40) + 0.33(3)(3)/N2 for N≥ 3, where the first error is statistical and the second is our estimate of the systematic error from all sources.