# QCD Thermodynamics on the Lattice from the Gradient Flow

## TL;DR

This paper introduces a lattice QCD method using gradient flow to accurately compute the energy-momentum tensor, enabling precise determination of bulk and transport properties of quark-gluon plasma with reduced computational complexity.

## Contribution

It presents a novel approach for calculating the renormalized energy-momentum tensor on the lattice via gradient flow, improving signal clarity and eliminating the need for wave function renormalization.

## Key findings

- Consistent results for interaction measure and thermal entropy with existing methods
- Successful measurement of two-point functions related to transport coefficients
- Comparison of numerical costs between different fermion flow methods

## Abstract

To obtain the precise values of the bulk quantities and transport coefficients in quark-gluon-plasma phase, we propose that a direct calculation of the renormalized energy-momentum tensor (EMT) on the lattice using the gradient flow. From one-point function of EMT, authors in Ref.[1] obtained the interaction measure and thermal entropy. The results are consistent with the one obtained by the integral method. Based on the success, we try to measure the two-point function of EMT, which is related to the transport coefficients. Advantages of our method are (1) a clear signal because of the smearing effects of the gradient flow and (2) no need to calculate the wave function renormalization of EMT. In addition, we give a short remark on a comparison of the numerical cost between the positive- and adjoint-flow methods for fermions, needed to obtain the EMT in the (2+1) flavor QCD.