Half-Skyrmion Hadronic Matter at High Density

Abstract

The hadronic matter described as a skyrmion matter embedded in an FCC crystal is found to turn into a half-skyrmion matter with vanishing (in the chiral limit) quark condensate and {\em non-vanishing} pion decay constant at a density $n_{1/2S}$ lower than or at the critical density $n_c^{\chi SR}$ at which hadronic matter changes over to a chiral symmetry restored phase with deconfined quarks. When hidden local gauge fields and dilaton scalars -- one "soft" and one "hard" -- are incorporated, this phase is characterized by $a=1$, $f_\pi\neq 0$ with the hidden gauge coupling $g\neq 0$ but $\ll 1$. While chiral symmetry is restored in this region in the sense that $\la\bar{q}q\ra=0$, quarks are still confined in massive hadrons and massless pions. This phase seems to correspond to the "quarkyonic phase" predicted in large $N_c$ QCD. It also represents the "hadronic freedom" regime relevant to kaon condensation at compact-star density. As $g\to 0$ (in the chiral limit), the symmetry "swells" -- as an emergent symmetry due to medium -- to $SU(N_f)^4$ as proposed by Georgi for the "vector limit." The fractionization of skyrmion matter into half-skyrmion matter is analogous to what appears to happen in condensed matter in (2+1) dimensions where half-skyrmions or "merons" enter as relevant degrees of freedom at the interface. Finally the transition from baryonic matter to color-flavor-locked quark matter can be bridged by a half-skyrmion matter.