Entanglement Enabled Tomography of Flux Tubes in (2+1)D Yang-Mills Theory

Abstract

We investigate the entangling properties of the color flux tube between a static quark-antiquark pair in pure gauge Yang-Mills theory. In earlier works, we defined a gauge-invariant flux tube entanglement entropy (FTE$^2$), the excess entanglement entropy of a region of gluon fields that can be attributed to the color flux tube, and demonstrated that it is finite in the continuum limit. FTE$^2$ was shown to have two contributions, one from the vibrations of the QCD string, and the other from its internal (color) degrees of freedom. In this work, we further explore the internal color component in (2+1)D Yang-Mills theory for $SU(N_c)$ gauge groups, varying $2\le N_c\le5$. We identify a novel physical scale in the theory, the entanglement radius $\xi_0$. This radius characterizes the transverse extent of the flux tube that must be completely severed by an entangling region to capture the entanglement entropy of color degrees of freedom. The key feature underlying this phenomenon is its topological nature. This is revealed through systematic studies of multi-slab entangling regions in which FTE$^2$ changes sharply when boundaries of the slabs completely cross-cut the flux tube. We find that $\xi_0$ increases approximately linearly with $N_c$ and is independent of both R\'{e}nyi replica number and the inter-quark separation length. We also study FTE$^2$ as a function of the entangling region's transverse displacement from the static quark pair and observe behavior consistent with a previously identified intrinsic width $\lambda$ of the flux tube, with an extracted value in agreement with the inverse mass of the lightest glueball for the gauge groups studied.