Remarks on nuclear matter: How an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ω</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> condensate can spike the speed of sound, and a model of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> baryons

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