Confinement in QCD: A Hybrid String Model with Vortex Corrections and Entanglement Entropy

Abstract: Confinement in Quantum Chromodynamics (QCD), binding quarks and gluons into hadrons, is characterized by a linear potential and the Wilson loop area law. We develop an analytical framework in $\text{SU(3)}$ gauge theory, proposing a hybrid effective string model that integrates chromoelectric flux tubes with topological corrections from (\mathbb{Z}_3) center vortices. Using strong-coupling expansion, we derive the Wilson loop expectation value, incorporating novel logarithmic vortex corrections, and compute a modified confining potential with non-universal terms. A central focus is the entanglement entropy of a confined quark-antiquark pair, modeled as a phase-damping quantum channel driven by the $\text{SU(3)}$ confining potential and vortex effects. We analytically demonstrate that confinement increases entropy, reflecting suppressed quantum correlations due to flux tube formation, with vortices enhancing decoherence. Our results are compared with holographic predictions. This work synthesizes $\text{SU(3)}$ gauge theory, topology, and quantum information, offering new insights into QCD confinement's quantum structure through a unique interplay of string dynamics, (\mathbb{Z}_3) vortices, and entanglement.