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

TL;DR

This paper examines discretization errors in energy-momentum tensor correlators in lattice gauge theory at finite temperature, highlighting the impact of lattice spacing and discretization choices on the accuracy of transport property calculations.

Contribution

It provides a detailed analysis of cutoff effects on various energy-momentum tensor correlators using lattice perturbation theory and Monte Carlo simulations, informing future lattice studies.

Findings

Correlator of energy density has larger discretization errors than momentum correlator.

Shear and stress correlators require lattice size $ t extgreater 8$ for reliable results.

Discretization errors on anisotropic lattices are comparable to isotropic lattices with similar spacing.

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 ${\bf p}$, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy $\int d^3x T_{00}$ has much larger discretization errors than the correlator of momentum $\int d^3x T_{0k}$. Secondly, the shear and diagonal stress correlators ($T_{12}$ and $T_{kk}$) require $\Nt\geq 8$ for the $Tx_0={1/2}$ 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 ${\bf p}$ correlators.