  It has been found that the topology effect and the possible emergent scale
and hidden local flavor symmetries at high density reveal a novel structure of
the compact star matter. The $N_f\geq2$ baryons can be described by the
skyrmion in the large $N_c$ limit and there is a robust topology change in the
skyrmion matter approach to dense nuclear matter. The hidden scale and local
flavor symmetries which are sources introducing the lightest scalar meson --
dilaton -- and lowest lying vector mesons into to nonlinear chiral effective
theory are seen to play important roles in understanding the nuclear force. We
review in this paper the generalized nuclear effective theory (G$n$EFT), which
applicable to nuclear matter from low density to the compact star density,
constructed with the robust conclusion from the topology approach to dense
matter and emergent scale and hidden local flavor symmetries. The topology
change at density larger than two times saturation density $n_0$ encoded in the
parameters of the effective field theory is interpreted as the hadron-quark
continuity in the sense of Cheshire Cat Principle. A novel feature predicted in
this theory that has not been found before is the precocious appearance of the
conformal sound velocity in the cores of massive stars, although the trace of
the energy-momentum tensor of the system is not zero. That is, in contrast to
the usual picture, the cores of massive stars are composed of quasiparticles of
fractional baryon charges, neither baryons nor deconfined quarks. Hidden scale
and local flavor symmetries emerge and give rise a resolution of the
longstanding $g_A$ quench problem in nuclei transition. To illustrate the
rationality of the GnEFT, we finally confront the generalized effective field
theory to the global properties of neutron star and the data from gravitational
wave detections.
