Quark-hadron continuity under rotation: Vortex continuity or boojum?

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 [1], 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.

Aharonov-Bohm defects

“…Two-gap superconductors can be in fact regarded as such an example of a gap composed of fermion-fermion condensation with a non-trivial AB phase. A non-Abelian vortex in dense QCD [28][29][30][31][32][33] provides a non-trivial AB phase for charged particles [34] as well as a Z 3 AB phase for quarks [35][36][37][38], and so if (further) diquark condensation forms, it may give a fermion example of AB defects.…”

“…Non-Abelian vortices in supersymmetric gauge theory [9][10][11][12][13][14][15][16][17][18][19][20][21] exhibit AB effects [22][23][24] including non-Abelian generalization of AB effects [25], once a part of flavor symmetry is gauged [26]. In dense QCD which may be relevant for cores of neutron stars, a color magnetic flux tube in the 2SC phase exhibits AB effects for quarks [27], while a non-Abelian vortex (color magnetic flux tube) in the color-flavor locked phase [28][29][30][31][32][33] also exhibits (electromagnetic) AB effects for charged particles [34] as well as Z 3 (color) AB effects for quarks [35][36][37][38].…”

Domain walls in neutron P23 superfluids in neutron stars

“…It has been known that, in a rotating neutron star, Abelian quantum superfluid vortices are created along the rotation axis in the hadron matter as well as non-Abelian quantum vortices (color magnetic flux tubes) in the quark matter [109][110][111][112][113]. Recently, the presence or absence of boojums have been discussed, which are defects at endpoints (or junction points) of these vortices at the interface [114][115][116][117][118]. The interactions between the domain walls and the boojum may influence the dynamics of neutron stars.…”

Effective gauge theories of superfluidity with topological order

“…At large baryon densities, QCD matter is expected to exhibit color color superconductivity [25][26][27][28][29], which has topological vortices [30][31][32][33]. Understanding the role of topology would be important in the discussion of the phase structure of dense nuclear matter [28,34,35] or the possible continuity of vortices between a nuclear superfluid and a color superconductor [36,37]. The low-energy theory of a color superconducting phase is described by a topological field theory coupled with massless Nambu-Goldstone (NG) bosons [34,35,38].…”