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<p>An exact solution of one-dimensional lattice gauge theory at finite temperature and non-zero chemical potential is reviewed for the gauge groups <i>G</i> = <i>Z</i>(<i>N</i>)<i>,</i> U(<i>N</i>)<i>,</i> SU(<i>N</i>) for all values of <i>N</i> and the number of fermion flavors <i>N</i><sub><i>f</i></sub>. 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 <i>N</i> = 2<i>,</i> 3 with one and two fermion flavors. In the large <i>N</i><sub><i>f</i></sub> limit we uncover the Roberge-Weiss phase transition and discuss its remnants at finite <i>N</i><sub><i>f</i></sub> . In the case of <i>N</i><sub><i>f</i></sub> degenerate flavors we also calculate 1) the large <i>N</i> limit, 2) the large <i>N</i><sub><i>f</i></sub> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月2日

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  • O. Borisenko,
  • V. Chelnokov,
  • S. Voloshyn,
  • P. Yefanov

摘要

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 Nf. 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 Nf limit we uncover the Roberge-Weiss phase transition and discuss its remnants at finite Nf . In the case of Nf degenerate flavors we also calculate 1) the large N limit, 2) the large Nf 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.