  I make two comments about nuclear matter. First, I consider the effects of a
coupling $\sim + \, \omega_\mu^2 \, \phi^2$ between the $\omega_\mu$ meson and
the $O(4)$ chiral field, $\phi$. A condensate for $\omega_0$ is automatically
generated at nonzero baryon density. 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
pion quantum spin liquid ($\pi$QSL) (arXiv:2005.10259 [hep-ph]). In this paper
I show that the $\pi$QSL 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.
