  In our continuing effort to understand hadronic matter at high density, we
have developed a unified field theoretic formalism for dense skyrmion matter
using a single Lagrangian to describe simultaneously both matter and meson
fluctuations and studied in-medium properties of hadrons. Dropping the quartic
Skyrme term, we incorporate into our previous Lagrangian the vector mesons rho
and omega in a form which is consistent with the symmetries of QCD. The results
that we have obtained, reported here, expose a hitherto unsuspected puzzle
associated with the role the omega meson plays at short distance. Since the
omega meson couples to baryon density, it leads to a pseudo-gap scenario for
the chiral symmetry phase transition, which is at variance with standard
scenario of QCD at the phase transition. We find that in the presence of the
omega mesons, the scale-anomaly dilaton field is prevented from developing a
vanishing vacuum expectation value at the chiral restoration, as a consequence
of which the in-medium pion decay constant does not vanish. This seems to
indicate that the omega degree of freedom obstructs the vector manifestation
which is considered to be a generic feature of effective field theories matched
to QCD.
