Topological structure of the entanglement radius of Yang-Mills flux tubes

TL;DR

This paper investigates the topological structure of the entanglement radius in (2+1)D Yang-Mills flux tubes, revealing how the flux tube's thickness influences entanglement entropy and its topological features.

Contribution

It provides detailed insights into the topological structure of the entanglement radius, expanding on previous work by analyzing geometries where the entanglement region size matches this radius.

Findings

Identifies the entanglement radius as a key physical scale in flux tube entanglement.

Shows the topological features of the entanglement radius influence entanglement entropy.

Provides detailed lattice geometry analysis related to flux tube entanglement.

Abstract

We expand on recent work arXiv:2601.17199 demonstrating the existence of a novel entanglement radius $\xi_0$ characterizing flux tube entanglement entropy (FTE$^2$) in (2+1)D Yang-Mills theory. This physical scale corresponds to the intrinsic thickness of the flux tube that must be fully severed by an entangling region for color degrees of freedom in the flux tube to contribute non-zero FTE$^2$. We consider here geometries of the entanglement region $V$ on the lattice where the length of the region cross-cutting the flux tube is of the same magnitude as $\xi_0$. Our results further the conclusions of arXiv:2601.17199 by adding detailed new information on the topological structure of the entanglement radius of color flux tubes.