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Color symmetry is spontaneously broken in quark matter at high density as aconsequence of di-quark condensations with exhibiting color superconductivity.Non-Abelian vortices or color magnetic flux tubes stably exist in thecolor-flavor locked phase at asymptotically high-density. The effectiveworldsheet theory of a single non-Abelian vortex was previously calculated inthe singular gauge to obtain the ${\mathbb C}P^2$ model [ arXiv:0908.4470 ,arXiv:0912.1352 ]. Here, we reconstruct the effective theory in a regular gaugewithout taking a singular gauge, confirming the previous results in thesingular gauge. As a byproduct of our analysis, we find that non-Abelianvortices in high-density QCD do not suffer from any obstruction for the globaldefinition of a symmetry breaking.

Low-energy Effective Worldsheet theory of a non-Abelian vortex in high-density QCD Revisited: A regular gauge construction