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Different types of non-Abelian vortex-strings appear in dense or hot QCD,both of which possess non-Abelian internal orientation zero modes. We calculatethe interaction between them and find the universal repulsion for dense QCD(color superconductivity) and the dependence on the orientations for hot QCD(chirally broken phase). This is a review article based on our papersarXiv:0708.4092 and arXiv:0708.4096.

Non-Abelian Strings in Hot or Dense QCD