Abstract
Quark-hadron continuity was proposed as crossover between hadronic matter and quark matter without a phase transition, based on the matching of the symmetry and excitations in both phases. In the limit of a light strange-quark mass, it connects hyperon matter and the color-flavor-locked (CFL) phase exhibiting color superconductivity. Recently, it was proposed that this conjecture could be generalized in the presence of superfluid vortices penetrating both phases (arXiv:1803.05115 [hep-ph]), and it was suggested that one hadronic superfluid vortex in hyperon matter could be connected to one non-Abelian vortex (color magnetic flux tube) in the CFL phase. Here, we argue that their proposal is consistent only at large distances; instead, we show that three hadronic superfluid vortices must combine with three non-Abelian vortices with different colors with the total color magnetic fluxes canceled out, where the junction is called a colorful boojum. We rigorously prove this in both a macroscopic theory based on the Ginzburg-Landau description in which symmetry and excitations match (including vortex cores), and a microscopic theory in which the Aharonov-Bohm phases of quarks around vortices match.
Highlights
The presence or absence of phase transitions is the most important issue to understand phases of matter
Particle component uB and the Λ hole component vB: ðuB; vBÞ → ðeiα=2uB; e−iα=2vBÞ. We find that this transformation satisfies the Bogoliubov–de Gennes (BdG) equation in Eq (B1) in Appendix B 1
In this paper we have discussed the continuity of vortices during the crossover between the hadronic and CFL phases
Summary
The presence or absence of phase transitions is the most important issue to understand phases of matter. Is not compatible with the symmetry structures of vortex cores—we reach the conclusion that arguably the only possibility left is to form a connection of three hadronic vortices in the hyperon matter of ΛΛ condensation with three NA vortices in the CFL phase, with the total color magnetic fluxes canceled out, forming a colorful boojum [24] analogous to a boojum in superfluid helium-3 [25,26] We prove this both in a macroscopic theory based on the Ginzburg-Landau (GL) description in which symmetry and excitations match including vortex cores, and a microscopic theory in which the Aharonov-Bohm (AB) phases of quarks around vortices match
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