Entanglement in Four-Dimensional SU(3) Gauge Theory

TL;DR

This paper presents the first non-perturbative lattice calculation of the entanglement entropy in four-dimensional SU(3) gauge theory, revealing conformal behavior at small scales and a decrease towards zero at larger scales.

Contribution

It provides the first non-perturbative computation of the entropic c-function in SU(3) gauge theory using lattice Monte Carlo methods and the replica technique.

Findings

Entropic c-function is nearly constant for 0 to 0.7 fm, indicating conformal invariance.

The constant value matches perturbative free gluon calculations within 20%.

The c-function decreases and approaches zero near 0.9 fm, reflecting confinement effects.

Abstract

We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic $c$-function ($C(l)$) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method. For $0 \leqslant l \leqslant 0.7$~fm, where $l$ is the length of the subspace, the entropic $c$-function is almost constant, indicating conformally invariant dynamics. The value of the constant agrees with that perturbatively obtained from free gluons, with 20 % discrepancy. When $l$ is close to the Hadronic scale, the entropic $c$-function decreases smoothly, and it is consistent with zero within error bars at $l \gtrsim 0.9$ fm.