Abstract
I make two comments about nuclear matter. First, I consider the effects of a coupling between the $O(4)$ chiral field, $\vec{\phi}$, and the $\omega_\mu$ meson, $\sim + \, \omega_\mu^2 \, \vec{\phi}^{\, 2}$; for any net baryon density, a condensate for $\omega_0$ is unavoidably generated. I assume that with increasing density, a decrease of the chiral condensate and the effective $\omega_0$ 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 "condensate" into a quantum pion liquid (Q$\pi$L) (arXiv:2005.10259). In this paper I show that the Q$\pi$L persists at zero temperature. If valid qualitatively at $N=4$, the $\omega_0$ mass goes up sharply and suppresses the $\omega_0$ 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.
Highlights
To determine the equation of state (EOS) for nuclear matter, effective models can be used for baryon densities, nB, up to and above that for nuclear saturation, nsat [1,2,3,4,5,6,7,8,9,10]
In the past few years, astronomical observations of neutron stars [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32] have provided a significant insight into the nuclear EOS at densities above nsat
Uð1ÞA symmetry survive at densities far above nsat, as indicated by an analysis using a dilute gas of instantons
Summary
To determine the equation of state (EOS) for nuclear matter, effective models can be used for baryon densities, nB, up to and above that for nuclear saturation, nsat [1,2,3,4,5,6,7,8,9,10]. In the past few years, astronomical observations of neutron stars [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32] have provided a significant insight into the nuclear EOS at densities above nsat. Excitations near the Fermi surface are dominated by color superconductivity [33,34,36]
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