Connecting dilaton thermal fluctuation with the Polyakov loop at finite temperature
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908408935874560 |
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| author | Sheng, Bing-Kai Ma, Yong-Liang |
| author_facet | Sheng, Bing-Kai Ma, Yong-Liang |
| contents | 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 $\mathrm{SU(N_{\mathrm{c}})}$ gauge systems at finite temperatures starting from the Coleman\textendash 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-$N_{\mathrm{c}}$ behaviors of the expectation value of the Polyakov loop. Notably, our findings predict the strongest first-order deconfinement phase transition as $N_{\mathrm{c}} \to +\infty$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13549 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connecting dilaton thermal fluctuation with the Polyakov loop at finite temperature Sheng, Bing-Kai Ma, Yong-Liang High Energy Physics - Phenomenology High Energy Physics - Lattice Nuclear Theory 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 $\mathrm{SU(N_{\mathrm{c}})}$ gauge systems at finite temperatures starting from the Coleman\textendash 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-$N_{\mathrm{c}}$ behaviors of the expectation value of the Polyakov loop. Notably, our findings predict the strongest first-order deconfinement phase transition as $N_{\mathrm{c}} \to +\infty$. 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. |
| title | Connecting dilaton thermal fluctuation with the Polyakov loop at finite temperature |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice Nuclear Theory |
| url | https://arxiv.org/abs/2506.13549 |