One-dimensional QCD at finite density and its ’t Hooft-Veneziano limit

An exact solution of one-dimensional lattice gauge theory at finite temperature and non-zero chemical potential is reviewed for the gauge groups G = Z(N), U(N), SU(N) for all values of N and the number of fermion flavors N_f. Calculated are the partition function, free energy, the Polyakov loop expectation values, baryon density, quark condensate, meson and baryon correlation functions. Detailed analysis of the exact solutions is done for N = 2, 3 with one and two fermion flavors. In the large N_f limit we uncover the Roberge-Weiss phase transition and discuss its remnants at finite N_f . In the case of N_f degenerate flavors we also calculate 1) the large N limit, 2) the large N_f limit and 3) the ’t Hooft-Veneziano limit of all models. The critical behavior of the models in these limits is studied and the phase structure is described in details. A comparison of all limits with U(3) and SU(3) QCD is also performed. In order to achieve these results we explore several representations of the partition function of one-dimensional QCD obtained and described in the text.