When cold, dense quarks in 1+1 and 3+1 dimensions are not a Fermi liquid

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.