Fractionized Skyrmions in Dense Compact-Star Matter

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 {\it non-vanishing} pion decay constant {$f_{\pi }$} at a density $n_{1\mathrm{/}2}$ lower than or near the critical density $n_c$ at which hadronic matter changes over to a chiral symmetry restored phase with possibly deconfined quarks. When hidden local gauge fields and a dilaton scalar of spontaneously broken scale symmetry with decay constant $f_{\chi }$ are incorporated, this half-skyrmion phase is characterized by $f_\chi\approx f_\pi\neq 0$withthehiddengaugecoupling$g\neq 0$but$\ll 1$. While chiral symmetry is restored {\it globally} in this region in the sense that space-averaged, $\text{la}\bar{q}q\text{ra}$ vanishes, quarks are still confined in massive hadrons and massless pions. This phase is shown to play a crucial role in the model for a smooth transition from a soft EoS at low density to a stiffer EoS at high density, the changeover taking place at $n_{1\mathrm{/}2}\sim 2n_0$. It resembles the “quarkyonic phase” predicted in large $N_c$ QCD and represents the “hadronic freedom” regime which figures as a doorway to chiral restoration. The fractionization of skyrmion matter into half-skyrmion matter has a tantalizing analogy 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.