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Cusp in the Symmetry Energy, Speed of Sound in Neutron Stars and Emergent Pseudo-Conformal Symmetry

We review how the "cusp" predicted in the nuclear symmetry energy generated by a topology change at density $n_{1/2}\gsim 2 n_0$ can have a surprising consequence, so far unrecognized in nuclear physics and astrophysics communities, on the structure of dense compact-star matter. The topology change, when translated into nuclear EFT with "effective" QCD degrees of freedom in terms of hidden local and scale symmetries duly taken into account, predicts an EoS that is soft below and stiff above $n\gsim n_{1/2}$, involving no low-order phase transitions, and yields the macrophysical properties of neutron stars consistent -- so far with no tension -- with the astrophysical observations, including the maximum mass $ 2.0\lsim M/ M_\odot\lsim 2.2$ as well as the GW data. Furthermore it describes the interior core of the massive stars populated by baryon-charge-fractionalized quasi-fermions that are neither baryonic nor quarkonic. It is argued that the cusp "buried" in the symmetry energy resulting from strong correlations with hidden heavy degrees of freedom leads, at $n\gsim n_{1/2}$, to what we dubbed "pseudo-conformal" sound speed, $v^2_{pcs}/c^2\approx 1/3$, precociously converged from below at $n_{1/2}$. It is not strictly conformal since the trace of energy-momentum tensor is not zero even in the chiral limit. This observation with the topology change identified with the putative hadron-quark continuity, taking place at at density $\gsim 2 n_0$, implies that the quantities accurately measured at $\sim n_0$ cannot give a stringent constraint for what takes place at the core density of compact stars $\sim (3-7) n_0$. This is because the change of degrees of freedom in effective field theory is involved. We discuss the implication of this on the recent PREX-II "dilemma" in the measured skin thickness of $^{208}$Pb.