  We explore the hadron properties in dense baryonic matter in a unified way by
using a Skyrme model constructed with an effective Lagrangian which includes
the $\rho$ 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. With
the two input values of pion decay constant and the lowest lying vector meson
mass which can be fixed in free space, all the other low energy constants in
the effective Lagrangian are determined by their master formulas derived from
holographic QCD models, which allows us to study the baryonic matter properties
with no additional free parameters and thus without ambiguities. We find that
the $\omega$ field that figures in the homogeneous Wess-Zumino term plays a
crucial role in the skyrmion structure and its matter properties. The most
striking and intriguing observation is that the pion decay constant that
smoothly drops with increasing density in the Skyrmion phase stops decreasing
at $n_{1/2}^{}$ at which the skyrmions in medium fractionize into
half-skyrmions and remains nearly constant in the half-skyrmion phase. In
accordance with the large $N_c$ consideration, the baryon mass also stays
non-scaling in the half-skyrmion phase. This feature is supported by the
nuclear effective field theory with the parameters of the Lagrangian scaling
modified at the skyrmion--half-skyrmion phase transition. Our exploration also
uncovers the crucial role of the $\omega$ meson in multi-baryon systems as well
as in the structure of a single skyrmion.
