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We use the Wilson flow to define the gauge anisotropy at a given physical scale. We demonstrate the use of the anisotropic flow by performing the tuning of the bare gauge anisotropy in the tree-level Symanzik action for several lattice spacings and target anisotropies. We use this method to tune the anisotropy parameters in full QCD, where we also exploit the diminishing effect of a well chosen smearing on the renormalization of the fermion anisotropy.
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The non-perturbative computation of the energy-momentum tensor can be used to study the scaling behaviour of strongly coupled quantum field theories. The Wilson flow is an essential tool to find a meaningful formulation of the energy-momentum tensor on the lattice. We extend recent studies of the renormalisation of the energy-momentum tensor in four-dimensional gauge theory to the case of a three-dimensional scalar theory to investigate its intrinsic structure and numerical feasibility on a more basic level. In this paper, we discuss translation Ward identities, introduce the Wilson flow for scalar theory, and present our results for the renormalisation constants of the scalar energy-momentum tensor.
We calculate the PCAC mass for $(2+1)$ flavor full QCD with Wilson-type quarks. We adopt the Small Flow-time eXpansion (SFtX) method based on the gradient flow which provides us a general way to compute correctly renormalized observables even if the relevant symmetries for the observable are broken explicitly due to the lattice regularization, such as the Poinc{a}re and chiral symmetries. Our calculation is performed on heavy $u, d$ quarks mass ($m_{pi}/m_{rho}simeq0.63$) and approximately physical $s$ quark mass with fine lattice $a simeq 0.07$~fm. The results are compared with those computed with the Schrodinger functional method.
We give a determination of the phenomenological value of the Wilson (or gradient) flow scales t0 and w0 for 2+1 flavours of dynamical quarks. The simulations are performed keeping the average quark mass constant, which allows the approach to the physical point to be made in a controlled manner. O(a) improved clover fermions are used and together with four lattice spacings this allows the continuum extrapolation to be taken.
Recently, we proposed a new method to extract the string tension from 4-dimensionally smeared Wilson loops. In this talk, we first show that the results obtained using this smearing method are identical to those obtained by Wilson flow, once the time step is sufficiently small. We then demonstrate the practical advantage of our method by applying it to the calculation of string tension in SU(3) Yang-Mills theory.
We study thermodynamic properties of 2+1 flavor QCD applying the Small Flow-time eXpansion (SFtX) method based on the gradient flow. The method provides us with a general way to compute correctly renormalized observables irrespective of explicit violation of symmetries due to the regularization, such as the Poincare and chiral symmetries on the lattice. We report on the status of our on-going project to compute the energy-momentum tensor and the chiral condensate at the physical point with improved Wilson quarks, extending our previous study with slightly heavy u and d quarks. We also report on our test of two-loop matching coefficients recently calculated by Harlander et al., revisiting the case of QCD with slightly heavy u and d quarks. Our results suggest that the SFtX method is powerful in extracting physical observables on the lattice.
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