Abstract
Quark-hadron continuity with two-flavor quarks that was proposed recently connects hadronic matter with neutron $^3P_2$ superfluidity and two-flavor dense quark matter. This two-flavor dense quark phase consists of the coexistence of the 2SC condensates and the $P$-wave diquark condensates of $d$-quarks, which gives rise to color superconductivity as well as superfluidity. We classify vortices in this phase. The most stable vortices are what we call the non-Abelian Alice strings, which are superfluid vortices with non-Abelian color magnetic fluxes therein, exhibiting so-called topological obstruction, or a non-Abelian generalization of the Alice property. We show that a single Abelian superfluid vortex is unstable against decay into three non-Abelian Alice strings. We discover that a non-Abelian Alice string carries orientational moduli of the real projective space $\mathbb{R}P^2$ corresponding to the color flux therein in the presence of the $P$-wave condensates alone. We calculate Aharanov-Bohm (AB) phases around the non-Abelian Alice string, and find that the 2SC condensates and string's orientational moduli must be aligned with each other because of single-valuedness of the AB phases of the 2SC condensates.
Highlights
Color superconductor is the ground state of the cold QCD matter at densities much higher than that of saturated nuclei n0 1⁄4 0.16 fm−3; the only known circumstance where we might find such kind of matter is in the core of neutron stars [1]
Various phases are known for color superconductivity such as color-flavor locked (CFL) phase [2] in three-flavor symmetric matter and 2-flavor superconducting (2SC) phase [3,4] in two-flavor symmetric matter
In the CFL phase, topologically stable superfluid vortex comes about owing to the nontrivial first homotopy group π11⁄2Uð1ÞB 1⁄4 Z [6,7]. It is related with the broken Uð1ÞB symmetry in the CFL phase, which is possible as the Vafa-Witten theorem does not apply at finite density [8]
Summary
Color superconductor is the ground state of the cold QCD matter at densities much higher than that of saturated nuclei n0 1⁄4 0.16 fm−3; the only known circumstance where we might find such kind of matter is in the core of neutron stars [1]. The recent insights from the neutron star observations, lead to the novel phase of color superconductivity in two-flavor matter with the broken Uð1ÞB symmetry [26] This phase is called the 2SC þ hddi phase. We describe that the most stable vortices in the hddi phase are non-Abelian vortices, which support 1=3 fractional windings in Uð1ÞB as well as the color-magnetic fluxes similar to those in the CFL phase These vortices exhibit the unique features akin to the so-called Alice strings [40,41,42,43,44,45,46,47,48,49,50], we named them as “non-Abelian Alice strings”.
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