Non-Abelian Alice strings in two-flavor dense QCD

TL;DR

This paper classifies and analyzes non-Abelian Alice strings in two-flavor dense QCD, revealing their stability, properties, and the interplay with condensates, advancing understanding of topological defects in color superconductivity.

Contribution

It introduces non-Abelian Alice strings in two-flavor dense QCD, demonstrating their stability, moduli space, and AB phase properties, which were not previously understood.

Findings

Single Abelian vortex decays into three non-Abelian Alice strings.

Non-Abelian Alice strings carry orientational moduli in $\,\mathbb{R}P^2$.

AB phases constrain the alignment of condensates and string moduli.

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.