I will outline 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 perturbed Wess-Zumino-Novikov-Witten (WZNW) model. At nonzero density, excitations near the Fermi surface form a non-Fermi (Luttinger) liquid. In the single-flavor case, integrability permits the numerically exact evaluation of the Luttinger parameter and the group velocity of excitations. In the $N_f>1$ case, these can be obtained perturbatively from the charge susceptibility. The non-FL behavior is potentially 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.
The talk is based on the following preprint:
ML, Robert Konik, Rob Pisarski, Alexei Tsvelik, arXiv:2112.10238v1 [hep-th].
Vladi Skokov