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

TL;DR

This paper reconstructs the effective worldsheet theory of non-Abelian vortices in high-density QCD in a regular gauge, confirming previous results and showing no obstruction to symmetry breaking.

Contribution

It provides a regular gauge derivation of the non-Abelian vortex worldsheet theory, validating earlier singular gauge findings and clarifying symmetry breaking properties.

Findings

Confirmed the ${ m CP}^2$ model in a regular gauge

Demonstrated no obstruction to global symmetry breaking

Validated previous singular gauge results

Abstract

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.