Internal color contributions to flux tube entanglement entropy

TL;DR

This paper investigates the internal color contributions to the entanglement entropy of flux tubes in (2+1)D Yang-Mills theory, exploring how geometry and color number affect the entropy's internal component.

Contribution

It extends previous work by analyzing different region geometries and boundary crossings, supporting the conjectured form of internal entropy with new numerical insights.

Findings

Internal entropy scales as $raket{F}\log(N_c)$ with boundary crossings.

Preliminary results confirm the conjectured entropy form across geometries.

Subtleties arise from flux tube intersections with the region boundary.

Abstract

In recent work arXiv:2410.00112, we introduced and computed entanglement entropy of the color flux tube (FTE$^2$) between a heavy quark-antiquark pair in (2+1)D Yang-Mills theory. Our numerical results suggest that FTE$^2$ can be partitioned into a component corresponding to transverse vibrations of the flux tube and an internal color entropy. Further, motivated by analytical (1+1)D calculations, and SU(2) (2+1)D Yang-Mills numerical results, we argued that the internal entropy takes the form $\langle F\rangle\log(N_c)$, with $\langle F\rangle$ the number of times, on average, that the flux tube crossed a boundary between region $V$ and its complement. We extend here our FTE$^2$ study to consider different geometries of region $V$, varying the number of boundary crossings, and number of colors. Our preliminary results support the conjectured form of the internal entropy, albeit with noteworthy subtleties relating to the partial/full intersections of the flux tube with the region $V$.