Abstract
We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields. We tune the action parameters based on torelon masses in moderate cubic physical volumes, and investigate the size of cut-off effects in other physical quantities, including torelon masses in asymmetric spatial volumes, the static quark potential, and gradient flow observables. In 2-d O(N) models similarly constructed nearest-neighbor actions have led to a drastic reduction of cut-off effects, down to the permille level, in a wide variety of physical quantities. In the gauge theories, we find significant reduction of lattice artifacts, and for some observables, the coarsest lattice result is very close to the continuum value. We estimate an improvement factor of 40 compared to using the Wilson gauge action to achieve the same statistical accuracy and suppression of cut-off effects. The simplicity of the gauge action makes it amenable for dynamical fermion simulations.
Highlights
2-d O(N) models share several features, including asymptotic freedom and a nonperturbatively generated mass gap, with 4-d non-Abelian gauge theories
We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields
We found that the improved action decreases the cut-off effects of many quantities including torelon masses on asymmetric lattices, the static potential, and observables related to the gradient flow of the gauge fields
Summary
The optimization of the action is done by moving along the β(γ) line to minimize the deviation of u110(L) ≡ m110(L)L from its continuum limit The latter was obtained by measuring the corresponding torelon masses at the same physical point u100(L) = u and finer resolutions with the Wilson action and extrapolating to a/L = 0. This way one obtains the pair of couplings (β, γ) which are optimal for this resolution (and the given choice of observables). At the chosen u value we measured the diagonal torelon state u110(L) on cubic spatial lattices of size L/a = 4, 6, 8, 10 using the Wilson action. We could make a more accurate determination for the continuum value of u110(L) with a constrained fit of Wilson and improved action data which demands that they have a common continuum limit, but that would not serve our purpose here to check for consistency between the two independent sets of simulations
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