  How the axial coupling constant $g_A$ in nuclear Gamow-Teller transitions
described in shell model gets "quenched" to a universal constant close to 1 can
be explained by nuclear correlations in Fermi-liquid fixed point theory using a
scale-symmetric chiral Lagrangian supplemented with hidden local symmetric
vector mesons. Contrary to what one might naively suspect -- and has been
discussed in some circles, there is no fundamental quenching at nuclear matter
density due to QCD condensates. When the density of many-body systems treated
with the same Lagrangian increases beyond the density $n=n_{1/2}\gsim 2n_0$
(where $n_0$ is the normal nuclear matter density) at which skyrmions
representing baryons fractionize to half-skyrmions, with the $\rho$ meson
driven toward the vector manifestation fixed point and a scalar meson $\sigma$
driven to the dilaton-limit fixed point with the nucleons parity-doubled, the
dense matter supports the "pseudo-conformal" sound velocity for $n\gsim
n_{1/2}$ while the trace of the energy momentum tensor remains non-vanishing. A
plausible interpretation is that this signals the emergence of scale symmetry
not explicitly present or hidden in QCD in the vacuum. The fundamental constant
$g_A$, unaffected by QCD condensates for $n< n_{1/2}$, does go to 1 as the
dilaton-limit fixed point is approached before arriving at chiral restoration,
but it is not directly related to the "quenched $g_A$" in nuclei which can be
explained as a Fermi-liquid fixed point quantity. The mechanism that produces a
precocious pseudo-conformal sound velocity is expected to impact on the tidal
deformability $\Lambda$ in gravity waves from coalescing neutron stars.
