Entanglement in four-dimensional SU(3) gauge theory

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 ≤ l ≤ 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 Λ-1QCD (∼ T-1c) scale, the entropic c-function decreases smoothly, and it is consistent with zero within error bars at l ≳ 0.9 fm.