Narrow Results

When hadron-quark continuity is formulated in terms of a topology change at a density higher than twice the nuclear matter density $(n_0)$, the core of massive compact stars can be described in terms of quasiparticles of fractional baryon charges, behaving neither like pure baryons nor like deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), emerge and give rise both to the long-standing “effective $g_A^{\ast }\approx 1$” in nuclear Gamow–Teller (GT) transitions at $\lesssim n_0$ and to the pseudo-conformal sound velocity $v_{\mathrm{\text{pcs}}}^2/c^2\approx 1/3$ at $\gtrsim 3n_0$. It is suggested that what has been referred to, since a long time, as “quenched $g_A$” in light nuclei reflects what leads to the dilaton-limit $g_A^{\mathrm{\text{DL}}}=1$ at near the (putative) infrared fixed point of scale invariance. These properties are confronted with the recent observations in GT transitions and in astrophysical observations.

Using a model spectral function of the electron, the Hall conductivity in the normal metallic state of the Pr${}_{2-x}$Ce_xCuO₄ (PCCO) superconductor is calculated neglecting the current vertex-correction. The result is qualitatively consistent with the experiment. Consequently, the reason becomes clear why the Fermi-liquid theory fails to explain the anomaly of the Hall conductivity. The inconsistency of the fluctuation-exchange approximation also becomes clear.