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<p>Understanding the character of the deconfinement phase transition is one of the fundamental challenges in particle physics. In this work, we derive a formula for the expectation value of the Polyakov loop — the order parameter of the deconfinement phase transition — in pure SU(N<sub>c</sub>) gauge systems at finite temperature starting from the Coleman–Weinberg-type effective potential encoding the trace anomaly of QCD. Our results are in good agreement with the Lattice QCD data and can effectively describe the large-<i>N</i><sub>c</sub> behaviors of the expectation value of the Polyakov loop. Notably, our findings predict the strongest first-order deconfinement phase transition as <i>N</i><sub>c</sub> → +<i>∞</i>. Furthermore, to establish a relation between the dilaton field and the Polyakov loop, we also derive the scale transformation rule for temperature based on quantum statistical mechanics. The results of this work may shed a light on the connection between deconfinement phase transition and evolution of scale symmetry in the thermal system.</p>

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Connecting dilaton thermal fluctuation with the Polyakov loop at finite temperature

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月7日

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  • Bing-Kai Sheng,
  • Yong-Liang Ma

摘要

Understanding the character of the deconfinement phase transition is one of the fundamental challenges in particle physics. In this work, we derive a formula for the expectation value of the Polyakov loop — the order parameter of the deconfinement phase transition — in pure SU(Nc) gauge systems at finite temperature starting from the Coleman–Weinberg-type effective potential encoding the trace anomaly of QCD. Our results are in good agreement with the Lattice QCD data and can effectively describe the large-Nc behaviors of the expectation value of the Polyakov loop. Notably, our findings predict the strongest first-order deconfinement phase transition as Nc → +∞. Furthermore, to establish a relation between the dilaton field and the Polyakov loop, we also derive the scale transformation rule for temperature based on quantum statistical mechanics. The results of this work may shed a light on the connection between deconfinement phase transition and evolution of scale symmetry in the thermal system.