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

Color symmetry is spontaneously broken in quark matter at high density as a consequence of di-quark condensations with exhibiting color superconductivity. Non-Abelian vortices or color magnetic flux tubes stably exist in the color-flavor locked phase at asymptotically high-density. The effective worldsheet theory of a single non-Abelian vortex was previously calculated in the 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 gauge without taking a singular gauge, confirming the previous results in the singular gauge. As a byproduct of our analysis, we find that non-Abelian vortices in high-density QCD do not suffer from any obstruction for the global definition of a symmetry breaking.