Non-perturbative Renormalization of the EMT in Full QCD

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 $β$ values at approximately the same temperature, aimed for the continuum limit.

Figures (6)

• Figure 1: The renormalization coefficient $c_1$ for various lattice spacings at fixed temperature (left). The renormalization coefficient $c_2$ measured at $T < T_c$ across different lattice spacings (right). Plots from LA.
• Figure 2: Possible Polyakov loop vacua $V_{1,2,3}$, and the quark twist angles for the Roberge-Weiss case (red) and our case (black) (left). Free fermionic pressure for the Polyakov-loop vacua $V_1$, $V_2$ and $V_3$ (right).
• Figure 3: The up quark contribution (left) and fermionic contribution (right) to the interaction measure.
• Figure 4: The gluonic contribution (left) and overall contribution (right) to interaction measure.
• Figure 5: The down-quark number density (left) and pressure (right) for $\beta = 7.373$ and $\beta = 7.596$.