  The half-skyrmions that appear in dense baryonic matter when skyrmions are
put on crystals modify drastically hadron properties in dense medium and affect
strongly the nuclear tensor forces, thereby influencing the equation of state
(EoS) of dense nuclear and asymmetric nuclear matter. The matter comprised of
half skyrmions has vanishing quark condensate but non-vanishing pion decay
constant and could be interpreted as a hadronic dual of strong-coupled quark
matter. We infer from this observation combined with certain predictions of
hidden local symmetry in low-energy hadronic interactionsa a set of new scaling
laws -- called "new-BR" -- for the parameters in nuclear effective field theory
controlled by renormalization-group flow. They are subjected to the EoS of
symmetric and asymmetric nuclear matter, and are then applied to nuclear
symmetry energies and properties of compact stars. The changeover from the
skyrmion matter to a half-skyrmion matter that takes place after the cross-over
density $n_{1/2}$ provides a simple and natural field theoretic explanation for
the change of the EoS from soft to stiff at a density above that of nuclear
matter required for compact stars as massive as $\sim 2.4M_\odot$. Cross-over
density in the range $1.5n_0 \lsim n_{1/2} \lsim 2.0 n_0$ has been employed,
and the possible skyrmion half-skyrmion coexistence {or cross-over} near
$n_{1/2}$ is discussed. The novel structure of {the tensor forces and} the EoS
obtained with the new-BR scaling is relevant for neutron-rich nuclei and
compact star matter and could be studied in RIB (rare isotope beam) machines.
