I make two comments about nuclear matter. First, I consider the effects of a coupling between the $O(4)$ chiral field, $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}$, and the ${\ensuremath{\omega}}_{\ensuremath{\mu}}$ meson, $\ensuremath{\sim}+{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}}^{2}{\ensuremath{\omega}}_{\ensuremath{\mu}}^{2}$; for any net baryon density, a condensate for ${\ensuremath{\omega}}_{0}$ is unavoidably generated. I assume that with increasing density, a decrease of the chiral condensate and the effective ${\ensuremath{\omega}}_{0}$ mass gives a stiff equation of state (EOS). In order to match that onto a soft EOS for quarkyonic matter, I consider an $O(N)$ field at large $N$, where at nonzero temperature quantum fluctuations disorder, any putative pion ``condensates'' into a quantum pion liquid ($\mathrm{Q}\ensuremath{\pi}\mathrm{L}$) [R. D. Pisarski et al., Phys. Rev. D 102, 016015 (2020)]. In this paper, I show that the $\mathrm{Q}\ensuremath{\pi}\mathrm{L}$ persists at zero temperature. If valid qualitatively at $N=4$, the ${\ensuremath{\omega}}_{0}$ mass goes up sharply and suppresses the ${\ensuremath{\omega}}_{0}$ condensate. This could generate a spike in the speed of sound at high density, which is of relevance to neutron stars. Second, I propose a toy model of a $Z(3)$ gauge theory with three flavors of fermions, where $Z(3)$ vortices confine fermions into baryons. In $1+1$ dimensions, this model can be studied numerically with present techniques, using either classical or quantum computers.

Remarks on nuclear matter: How an ω 0 condensate can spike the speed of sound, and a model of Z ( 3 ) baryons

When hadron-quark continuity is formulated in terms of a topology change at a density higher than twice the nuclear matter density (n0), the core of massive compact stars can be described in terms ...

Manifestation of hidden symmetries in baryonic matter: From finite nuclei to neutron stars

We discuss the "sheet structure" of compressed baryonic matter possibly present in massive compact stars in terms of quantum Hall droplets and skyrmions for baryons in medium. The theoretical framework is anchored on a generalized scale symmetric hidden local symmetry that encompasses standard nuclear effective field theory ($s$EFT) and can access the density regimes relevant to massive compact stars. It hints at a basically different, hitherto unexplored structure of the {\it densest} baryonic matter stable against collapse to black hole. Hidden scale symmetry and hidden local symmetry together in nuclear effective field theory are seen to play a potentially crucial role in providing the hadron-quark duality in compressed baryonic matter.

Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions In Compact-Star Matter

A domain-wall configuration of the η′ meson bounded by a string (called a pancake or a Hall droplet) is recently proposed to describe the baryons with spin Nc/2. In order to understand its baryon number as well as the flavor quantum number, we argue that the vector mesons (the ρ and ω mesons) should play an essential role for the consistency of the whole picture. We determine the effective theory of large-Nc QCD with Nf massless fermions by taking into account a mixed anomaly involving the θ-periodicity and the global symmetry. The anomaly matching requires the presence of a dynamical domain wall on which a $$ \mathrm{U}{\left({N}_f\right)}_{-{N}_c} $$
 Chern-Simons theory is supported. We consider the boundary conditions that should be imposed on the edge of the domain wall, and conclude that there should be a boundary term that couples the $$ \mathrm{U}{\left({N}_f\right)}_{-{N}_c} $$
 gauge field to the vector mesons. We discuss the impact on physics of the chiral phase transition and the relation to the “duality” of QCD.

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Vector mesons on the wall

We further explore a recent proposal that the vector mesons in QCD have a special role as Chern-Simons fields on various QCD objects such as domain walls and the one flavored baryons. We compute contributions to domain wall theories and to the baryon current coming from a generalized Wess-Zumino term including vector mesons. The conditions that lead to the expected Chern-Simons terms and the correct spectrum of baryons, coincide with the conditions for vector meson dominance. This observation provides a theoretical explanation to the phenomenological principle of vector dominance, as well as an experimental evidence for the identification of vector mesons as the Chern-Simons fields. By deriving the Chern-Simons theories directly from an action, we obtain new results about QCD domain walls. One conclusion is the existence of a first order phase transition between domain walls as a function of the quarks' masses. We also discuss applications of our results to Seiberg duality between gluons and vector mesons and provide new evidence supporting the duality.

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Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term

When hadron-quark continuity is formulated in terms of a topology change at a density higher than twice the nuclear matter densiy $n_0$ the core of massive compact stars can be described in terms of quasiparticles of fractional baryon charges, behaving neither like pure baryons nor deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), emerge and give rise to the long-standing quenched $g_A$ in nuclear Gamow-Teller transitions at $\sim n_0$ and to the pseudo-conformal sound velocity $v_{pcs}^2/c^2\approx 1/3$ at $\gsim 3n_0$. These properties are confronted with the recent observations in superallowed Gamow-Teller transitions and in astrophysical observations.

What's in the core of massive neutron stars?

We describe the on-going effort to formulate the baryon-quark continuity in terms of a topology change in the equation of state (EoS) of dense baryonic matter in analogy to -- and inspired by -- the mapping of the characteristics of Chern-Simon topological field theory to Kohn-Sham density functional theory in the fractional quantized Hall effect (FQHE). This is done by translating the density-dependent characteristics of the skyrmion-half-skyrmion transition formulated in the presence of hidden local symmetry and (hidden) scale symmetry to the density-dependent parameters of a renormalization-group approach to Fermi-liquid fixed point theory. Predictions made in finite nuclei and infinite compact-star matter are presented.

Yong-Liang Ma

Papers

Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions In Compact-Star Matter

What's in the core of massive neutron stars?

Mapping topology to nuclear dilaton-HLS effective field theory for dense baryonic matter