Distribution of Stress Tensor around Static Quark--Anti-Quark from Yang-Mills Gradient Flow

TL;DR

This paper uses the Yang-Mills gradient flow to analyze the stress tensor distribution around a quark-antiquark pair in lattice gauge theory, revealing detailed flux tube structures and deriving the confining potential.

Contribution

It introduces a gauge-invariant method to compute the stress tensor distribution around static quarks using Yang-Mills gradient flow, providing new insights into flux tube structure.

Findings

Detailed flux tube structure along longitudinal and transverse directions.

Confining potential derived directly from local stress tensor.

Stress tensor well-defined via Yang-Mills gradient flow.

Abstract

The spatial distribution of the stress tensor around the quark--anti-quark ($Q\bar{Q}$) pair in SU(3) lattice gauge theory is studied. The Yang-Mills gradient flow plays a crucial role to make the stress tensor well-defined and derivable from the numerical simulations on the lattice. The resultant stress tensor with a decomposition into local principal axes shows, for the first time, the detailed structure of the flux tube along the longitudinal and transverse directions in a gauge invariant manner. The linear confining behavior of the $Q\bar{Q}$ potential at long distances is derived directly from the integral of the local stress tensor.