  It is shown that explicitly broken scale symmetry is essential for dense
skyrmion matter in hidden local symmetry theory. Consistency with the vector
manifestation fixed point for the hidden local symmetry of the lowest-lying
vector mesons and the dilaton limit fixed point for scale symmetry in dense
matter is found to require that the anomalous dimension ($\gamma_{G^2}$) of the
gluon field strength tensor squared ($G^2$) that represents the quantum trace
anomaly should be $0 <\gamma_{G^2} <3$.
