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arXiv · 2410.02328

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

O. Borisenko·V. Chelnokov·S. Voloshyn·P. Yefanov
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Abstract

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.

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O. Borisenko, V. Chelnokov, S. Voloshyn, P. Yefanov. 2024-10-03. One-dimensional QCD at finite density and its 't Hooft-Veneziano limit. https://arxiv.org/abs/2410.02328

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