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Interaction between Vortices in CFL Phase

We try to calculate the interaction between vortices in the color-flavor locked (CFL) phase of Quantum Chromodynamics (QCD). The most fundamental strings in high density color superconductivity are the non-abelian semi-super fluid strings. Using Abrikosov ansatz, one can show that the interaction between these vortices has a universal repulsion form when they are far from each other. The Ginzburg-Landau (GL) Lagrangian of CFL phase may be compared with the Lagrangian of Quantum Electrodynamics (QED) with three condensation states. The behavior of vortices of multi-component superconductivity, within the framework of GL theory was done for two condensation states ($\rm{MgB_2}$ superconductors) by variational method. The interaction between these vortices is attractive when they are far from each other and repulsive when they get close. We attempt to obtain the interaction between these vortices in such substances using numerical variational method for three condensation states (Fe-based superconductors). The ultimate aim of the research is to apply these calculations to the vortices in the color-flavor locked phase of QCD to be able to study the interaction between them.