Fermion structure of non-Abelian vortices in high density QCD

TL;DR

This paper investigates the microscopic structure of non-Abelian vortices in high-density QCD, revealing localized massless quark modes and their velocity behavior at different chemical potentials, using the Bogoliubov-de Gennes equation.

Contribution

It provides a detailed analysis of quark spectra in non-Abelian vortices via the B-dG equation, highlighting the existence of zero modes and their velocity dependence on chemical potential.

Findings

Massless quark modes are localized around vortices.

Velocities of these modes decrease with increasing chemical potential.

Low-energy excitations are effectively 1+1 dimensional massless fermions.

Abstract

We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the Color-Flavor-Locked phase whose symmetry SU(3)_{c+L+R} is further broken to SU(2)_{c+L+R} x U(1)_{c+L+R} at the vortex cores. Microscopic structure of vortices at scales shorter than the coherence length can be analyzed by the Bogoliubov-de Gennes (B-dG) equation (rather than the Ginzburg-Landau equation). We obtain quark spectra from the B-dG equation by treating the diquark gap having the vortex configuration as a background field. We find that there are massless modes (zero modes) well-localized around a vortex, in the triplet and singlet states of the unbroken symmetry SU(2)_{c+L+R} x U(1)_{c+L+R}. The velocities v_i of the massless modes (i=t,s for triplet and singlet) change at finite chemical potential \mu, and decrease as \mu becomes large. Therefore, low energy excitations in the vicinity of the vortices are effectively described by 1+1 dimensional massless fermions whose velocities are reduced v_i<1.