The energy-momentum tensor in lattice QCD and the Equation of State

TL;DR

This paper introduces a new non-perturbative renormalization method for the energy-momentum tensor in lattice QCD using shifted boundary conditions, enabling direct calculation of QCD thermodynamic properties.

Contribution

It develops a novel strategy for non-perturbative renormalization of the energy-momentum tensor in lattice QCD, validated at 1-loop order and applicable to high-temperature QCD simulations.

Findings

Renormalization constants determined at 1-loop order.

Entropy density related to energy-momentum tensor expectation values.

Feasibility demonstrated for high-temperature QCD simulations.

Abstract

We present a new theoretical and practical strategy to renormalize non-perturbatively the energy-momentum tensor in lattice QCD based on the framework of shifted boundary conditions. As a preparatory step for the fully non-perturbative calculation, we apply the strategy at 1-loop order in perturbation theory determining the renormalization constants of both the gluonic and the fermionic components of the energy-momentum tensor. Using shifted boundary conditions, the entropy density of QCD is directly related to the expectation value of the space-time components of the renormalized energy-momentum tensor. We then discuss its practical implementation by numerical simulations of QCD with 3 flavours of Wilson quarks for temperatures between 2.5 GeV and 80 GeV.