Cutoff Effects on Energy-Momentum Tensor Correlators in Lattice Gauge Theory

Abstract

We investigate the discretization errors affecting correlators of the energy-momentum tensor $T_{\mu \nu }$ at finite temperature in SU($N_c$) gauge theory with the Wilson action and two different discretizations of $T_{\mu \nu }$. We do so by using lattice perturbation theory and non-perturbative Monte-Carlo simulations. These correlators, which are functions of Euclidean time $x_0$ and spatial momentum $\mathbf{p}$, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy $\int d^{3}x{T}_{00}$ has much larger discretization errors than the correlator of momentum $\int d^{3}x{T}_{0k}$. Secondly, the shear and diagonal stress correlators ($T_{12}$ and $T_{kk}$) require $\Nt\geq 8$ for the $T{x}_0=1/2$ point to be in the scaling region and the cutoff effect to be less than 10%. We then show that their discretization errors on an anisotropic lattice with $\as/\at=2$ are comparable to those on the isotropic lattice with the same temporal lattice spacing. Finally, we also study finite $\mathbf{p}$ correlators.

16 pages, 5 figures

References in corpus (6)

• Finite Temperature Spectral Densities of Momentum and R-Charge Correlators in $\mathbb{N}=4$ Yang Mills Theory
• Energy-momentum tensor correlators and spectral functions
• Gluon contributions to the pion mass and light cone momentum fraction
• Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature
• Density, short-range order and the quark-gluon plasma
• Computing the viscosity of the QGP on the lattice

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• Implications of Poincare symmetry for thermal field theories in finite-volume
• The second order hydrodynamic transport coefficient $\kappa$ for the gluon plasma from the lattice
• Lattice study of a magnetic contribution to heavy quark momentum diffusion
• Viscosity of pure-glue QCD from the lattice
• Study of shear viscosity of SU (2)-gluodynamics within lattice simulation
• Consistency of field-theoretical and kinetic calculations of viscous transport coefficients for a relativistic fluid
• Lattice $B$-field correlators for heavy quarks
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• High statistics lattice study of stress tensor correlators in pure $SU(3)$ gauge theory