One-dimensional QCD at finite density and its ’t Hooft-Veneziano limit
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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2025)008 |
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| Summary: | 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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| ISSN: | 1029-8479 |