Hidden Local Symmetry and Dense Half-Skyrmion Matter

Understand

Transition from baryonic matter to color-flavor-locked quark matter is described in terms of skyrmion matter changing into half-skyrmion matter.

• The intermediate phase between the density $n_p$ at which a skyrmion turns into two half skyrmions and the chiral transition density $n_c^{\chi SR}$ at which hadronic matter changes over to quark matter corresponds to a chiral symmetry restored phase characterized by a vanishing quark condensate and a {\em non-vanishing} pion decay constant.
• When hidden local fields are incorporated, the vector manifestation of Harada-Yamawaki HLS theory implies that as density approaches $n_c^{\chi SR}$, the gauge coupling $g$ goes to zero (in the chiral limit) and the symmetry "swells" to $SU(N_f)^4$ as proposed by Georgi for the "vector limit." This enhanced symmetry, not present in QCD, can be interpreted as "emergent" in medium due to collective excitations.
• The fractionization of skyrmions into half-skyrmions resembles closely the magnetic N\'eel--to-valence bond solid (VBS) paramagnet transition where "baby" half-skyrmions enter as relevant degrees of freedom in the intermediate phase.