Non-perturbative Renormalization of the EMT in Full QCD

TL;DR

This paper develops a non-perturbative method to renormalize the energy-momentum tensor in full QCD on the lattice, enabling precise calculations of thermodynamic and transport properties.

Contribution

It introduces a novel non-perturbative renormalization approach for the EMT in full QCD, addressing lattice symmetry breaking issues and aiding in accurate transport coefficient determination.

Findings

Constructed the EMT for pure-gauge and full QCD on the lattice.

Analyzed thermodynamic quantities with imaginary chemical potential across multiple β values.

Provided a framework for continuum limit extrapolation of lattice QCD thermodynamics.

Abstract

The energy-momentum tensor (EMT) is the conserved current corresponding to space-time translation symmetry. Its applications are remarkably diverse, ranging from the thermodynamics to the calculation of transport coefficients. While the EMT is well-defined in the continuum up to a total derivative, with its coefficients fixed by Ward identities, its extension to lattice QCD is not straightforward. The primary challenge arises from the breaking of continuous space-time symmetries by the discrete lattice regulator. Although the EMT can be constructed on the lattice in a way that yields the correct continuum limit, the operators are not uniquely defined. In this proceeding, we construct the EMT for both pure-gauge theory and full QCD, discussing its renormalization in the specific context of determining the coefficients required for shear viscosity. In this context, we present a comparative analysis of the trace anomaly, number density, pressure, energy density and enthalpy density with imaginary chemical potential for multiple $\beta$ values at approximately the same temperature, aimed for the continuum limit.