  We analyze the behavior of quarks coupled to a $SU(N_c)$ gauge theory in 1+1
dimensions. In the limit of strong coupling, the model reduces to a
Wess-Zumino-Novikov-Witten (WZNW) model. At nonzero density, excitations near
the Fermi surface form a non-Fermi liquid. With $N_f$ flavors, the finite
density of quarks reduce to a free $U(1)$ field, which governs fluctuations in
baryon number, together with a WZNW $SU(N_f)$ nonlinear sigma model at level
$N_c$, from the pion/kaon modes. We compute the singularity in the charge
susceptibility at the Fermi surface and the attendant power law correlations.
We suggest that this is relevant to the quarkyonic regime of cold, dense QCD in
3+1 dimensions, in the limit that the Fermi surface is covered by many small
patches, and the theory is effectively one dimensional. In this regime the
dominant excitations near the Fermi surface are not baryons, but gapless
bosonic modes.
