Quarks and Compact Stars (QCS)
Oct. 20-22, 2014, KIAA at Peking University, Beijing - P. R. China


Invited Talk

Non-Abelian vortex lattice in dense QCD

Eiji Nakano

Department of Physics, Kochi University

Abstract: High density limit of QCD is very likely to be a color superconducting phase: the color-flavor locking phase (CFL phase). It is recently found that the most fundamental vortex in the CFL phase is a non-Abelian vortex (NAV). The usual Abelian vortex considered so far, which is associated with breaking of Baryon number $U(1)_B$ symmetry, is unstable to decay into the three NAVs. NAV has a nature of both global $U(1)_B$ vortex and a gauge vortex of color $SU(3)$. As a prominent feature of the NAV there appears a NG mode (an orientation mode), which is almost localized along the vortex `core' (`line' in case of vortex string). The orientation mode is described in terms of $1+1$ dimensional non-linear sigma model, and corresponds,in classical picture, to a specific color of gauge flux in the vortex core. However, strong quantum effects in the lower dimension break this color ordering of the single vortex; Coleman-Mermin-Wagner theorem. In this study we show that a lattice of NAV in rotating systems exhibits indeed a color ordering (color magnetism): if a spatially rotating system as in core of compact star is considered, and many NAVs are generated. Then, these vortices form a triangle lattice by vortex-vortex repulsion ($U(1)$ phonon exchange), and a sub-leading gauge interaction, which acts among orientation modes of vortex sites, leads to the color ordering, where the effective theory becomes an anisotropic $3+1$ dimensional non-linear sigma model.