Non-Abelian Strings in High Density QCD: Zero Modes and Interactions

TL;DR

This work analyzes non-Abelian semi-superfluid strings in the CFL phase of high-density QCD within a Ginzburg-Landau framework, showing that orientational zero modes form a normalizable $\mathbf{C}P^{N-1}$ moduli space and that two parallel strings experience a universal repulsive interaction, with a magnitude suppressed by a factor of $1/N$ relative to Abelian $U(1)_{\rm B}$ vortices. The interaction is independent of the relative orientation due to gauge equivalences at large distances, implying that $U(1)_{\rm B}$ vortices are unstable to decay into $N$ non-Abelian strings and that CFL matter remains stable under external color fields. The analysis combines explicit string solutions, orientational moduli, and an Abrikosov-type interaction calculation to reveal robust, orientation-insensitive long-range forces with potential implications for the structure of dense quark matter in astrophysical settings. These results constrain the possible topological configurations in color superconductors and suggest observable consequences for neutron star phenomenology and the behavior of dense QCD matter under external color fields.

Abstract

The most fundamental strings in high density color superconductivity are the non-Abelian semi-superfluid strings which have color gauge flux tube but behave as superfluid vortices in the energetic point of view. We show that in addition to the usual translational zero modes, these vortices have normalizable orientational zero modes in the internal space, associated with the color-flavor locking symmetry broken in the presence of the strings. The interaction among two parallel non-Abelian semi-superfluid strings is derived for general relative orientational zero modes to show the universal repulsion. This implies that the previously known superfluid vortices, formed by spontaneously broken U(1)_B, are unstable to decay. Moreover, our result proves the stability of color superconductors in the presence of external color gauge fields.

Figures (1)

• Figure 1: Configuration of two semi-superfluid strings with interval $2a$ in the polar coordinates $(\rho, \theta)$. $\rho_{1,2}$ is distance from string $\phi_{1,2}$, and $\theta_{1,2}$ is angle around it.