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We explore the hadron properties in dense baryonic matter in a unified way byusing a Skyrme model constructed with an effective Lagrangian which includesthe $\rho$ and $\omega$ vector mesons as hidden gauge bosons and is valid up to$O(p^4)$ in chiral expansion including the homogeneous Wess-Zumino terms. Withthe two input values of pion decay constant and the lowest lying vector mesonmass which can be fixed in free space, all the other low energy constants inthe effective Lagrangian are determined by their master formulas derived fromholographic QCD models, which allows us to study the baryonic matter propertieswith no additional free parameters and thus without ambiguities. We find thatthe $\omega$ field that figures in the homogeneous Wess-Zumino term plays acrucial role in the skyrmion structure and its matter properties. The moststriking and intriguing observation is that the pion decay constant thatsmoothly drops with increasing density in the Skyrmion phase stops decreasingat $n_{1/2}^{}$ at which the skyrmions in medium fractionize intohalf-skyrmions and remains nearly constant in the half-skyrmion phase. Inaccordance with the large $N_c$ consideration, the baryon mass also staysnon-scaling in the half-skyrmion phase. This feature is supported by thenuclear effective field theory with the parameters of the Lagrangian scalingmodified at the skyrmion--half-skyrmion phase transition. Our exploration alsouncovers the crucial role of the $\omega$ meson in multi-baryon systems as wellas in the structure of a single skyrmion.

Skyrmions, half-skyrmions and nucleon mass in dense baryonic matter