Entanglement entropy of a color flux tube in (1+1)D Yang-Mills theory

TL;DR

This paper analytically computes the entanglement entropy of a color flux tube in (1+1)D Yang-Mills theory, revealing it depends only on crossing number and color representation, not on string length.

Contribution

It provides the first analytical calculation of flux tube entanglement entropy in (1+1)D Yang-Mills, highlighting its dependence on crossing number and color representation.

Findings

FTE$^2$ depends only on crossing number and color representation.

The result is independent of the placement of branching points.

Analytical computation complements previous numerical results in higher dimensions.

Abstract

In recent work arxiv:2410.00112 , we computed a novel flux tube entanglement entropy (FTE$^2$) of the color flux tube stretched between a heavy quark-antiquark pair on a Euclidean lattice in (2+1)D Yang-Mills theory. Our numerical results suggested that FTE$^2$ can be partitioned into an internal color entanglement entropy and a vibrational entropy corresponding to the transverse excitations of a QCD string, with the latter described by a thin string model. Since the color flux tube does not have transverse excitations in (1+1)D, we analytically compute the contribution of the internal color degrees of freedom to FTE$^2$ in this simpler framework. For the multipartite partitioning of the color flux tube, we find the remarkable result that FTE$^2$ only depends on the number of times the flux tube crosses the border between two spatial regions, and the dimension of the representation of the color group, but not on the string length. The result holds independently of whether the branching points are placed on the vertices of the lattice or in the center of plaquettes.