We study the stress-tensor distribution around the flux tube in static quark and anti-quark systems based on the momentum conservation and the Abelian-Higgs (AH) model. We first investigate constraints on the stress-tensor distribution from the momentum conservation and show that the effect of boundaries plays a crucial role to describe the structure of the flux tube in SU(3) Yang-Mills theory which has measured recently on the lattice. We then study the distributions of the stress tensor and energy density around the magnetic vortex with and without boundaries in the AH model, and compare them with the distributions in SU(3) Yang-Mills theory based on the dual superconductor picture. It is shown that a wide parameter range of the AH model is excluded by a comparison with the lattice results in terms of the stress tensor.
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