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Register a new userCorrelations of Energy-Momentum Tensor via Gradient Flow in SU(3) Yang-Mills Theory at Finite Temperature
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Euclidean two-point correlators of the energy-momentum tensor (EMT) in SU(3) gauge theory on the lattice are studied on the basis of the Yang-Mills gradient flow. The entropy density and the specific heat obtained from the two-point correlators are shown to be in good agreement with those from the one-point functions of EMT. These results constitute a first step toward the first principle simulations of the transport coefficients with the gradient flow.
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The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with $beta=6.287$--$7.500$ corresponding to the lattice spacing $a= 0.013$--$0.061,mathrm{fm}$. The spatial (temporal) sizes are chosen to be $N_s= 64$, $96$, $128$ ($N_{tau}=12$, $16$, $20$, $22$, $24$) with the aspect ratio, $5.33 le N_s/N_{tau} le 8$. Double extrapolation, $arightarrow 0$ (the continuum limit) followed by $trightarrow 0$ (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.
Energy momentum tensor (EMT) characterizes the response of the vacuum as well as the thermal medium under the color electromagnetic fields. We define the EMT by means of the gradient flow formalism and study its spatial distribution around a static quark in the deconfined phase of SU(3) Yang-Mills theory on the lattice. Although no significant difference can be seen between the EMT distributions in the radial and transverse directions except for the sign, the temporal component is substantially different from the spatial ones near the critical temperature $T_c$. This is in contrast to the prediction of the leading-order thermal perturbation theory. The lattice data of the EMT distribution also indicate the thermal screening at long distance and the perturbative behavior at short distance.
Using finite size scaling techniques and a renormalization scheme based on the Gradient Flow, we determine non-perturbatively the $beta$-function of the $SU(3)$ Yang-Mills theory for a range of renormalized couplings $bar g^2sim 1-12$. We perform a detailed study of the matching with the asymptotic NNLO perturbative behavior at high-energy, with our non-perturbative data showing a significant deviation from the perturbative prediction down to $bar{g}^2sim1$. We conclude that schemes based on the Gradient Flow are not competitive to match with the asymptotic perturbative behavior, even when the NNLO expansion of the $beta$-function is known. On the other hand, we show that matching non-perturbatively the Gradient Flow to the Schrodinger Functional scheme allows us to make safe contact with perturbation theory with full control on truncation errors. This strategy allows us to obtain a precise determination of the $Lambda$-parameter of the $SU(3)$ Yang-Mills theory in units of a reference hadronic scale ($sqrt{8t_0},Lambda_{overline{rm MS}} = 0.6227(98)$), showing that a precision on the QCD coupling below 0.5% per-cent can be achieved using these techniques.
We study the pressure anisotropy in anisotropic finite-size systems in SU(3) Yang-Mills theory at nonzero temperature. Lattice simulations are performed on lattices with anisotropic spatial volumes with periodic boundary conditions. The energy-momentum tensor defined through the gradient flow is used for the analysis of the stress tensor on the lattice. We find that a clear finite-size effect in the pressure anisotropy is observed only at a significantly shorter spatial extent compared with the free scalar theory, even when accounting for a rather large mass in the latter.
We study the infrared behavior of the effective Coulomb potential in lattice SU(3) Yang-Mills theory in the Coulomb gauge. We use lattices up to a size of 48^4 and three values of the inverse coupling, beta=5.8, 6.0 and 6.2. While finite-volume effects are hardly visible in the effective Coulomb potential, scaling violations and a strong dependence on the choice of Gribov copy are observed. We obtain bounds for the Coulomb string tension that are in agreement with Zwanzigers inequality relating the Coulomb string tension to the Wilson string tension.
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