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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.08735 |
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| _version_ | 1866909993013346304 |
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| author | Deppman, Airton |
| author_facet | Deppman, Airton |
| contents | The deconfining transition in $SU(3)$ gauge theory, traditionally interpreted through the Gross-Witten-Wadia (GWW) model as a sharp third-order phase transition in the large-$N_c$ limit, appears as a smooth crossover in lattice QCD. This work demonstrates that the transition is topologically smoothed into a crossover by incorporating the fractal momentum space structure inherent to thermofractals. By matching the non-extensive $β$-function to one-loop QCD results, a fundamental scaling of the thermofractal index $q$ is derived as a function of the number of flavours $N_f$. It is proven that applying a $q$-deformed derivative operator $\mathcal{D}_q$ to the $q$-logarithm of the eigenvalue distance results in a non-extensive measure that effectively smears the topological stiffness of the gauge vacuum. A unified master equation for the Polyakov loop $\langle L \rangle$ is presented, governed by the thermofractal index $q$ and a single variance parameter $σ^2(T)$ that scales as $T^{1/(q-1)}$. The observed phase dynamics are shown to be asymptotic limits of this unified density: a ``soft'' algebraic growth $\langle L \rangle \propto T^{11}$ in the 1D string-like confined regime for $N_f=0$, and a rapid $1 - \langle L \rangle \propto T^{-21}$ suppression in the 3D deconfined volume for $N_f=3$. This approach provides a microscopic foundation for partial deconfinement theory and reproduces lattice QCD data with a reduced $χ^2 \approx 1.12$, offering a rigorous reconciliation between matrix model topology and the continuous QCD crossover. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08735 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | QCD phase-transition under the light of Thermofractal Deppman, Airton High Energy Physics - Lattice High Energy Physics - Experiment High Energy Physics - Phenomenology High Energy Physics - Theory The deconfining transition in $SU(3)$ gauge theory, traditionally interpreted through the Gross-Witten-Wadia (GWW) model as a sharp third-order phase transition in the large-$N_c$ limit, appears as a smooth crossover in lattice QCD. This work demonstrates that the transition is topologically smoothed into a crossover by incorporating the fractal momentum space structure inherent to thermofractals. By matching the non-extensive $β$-function to one-loop QCD results, a fundamental scaling of the thermofractal index $q$ is derived as a function of the number of flavours $N_f$. It is proven that applying a $q$-deformed derivative operator $\mathcal{D}_q$ to the $q$-logarithm of the eigenvalue distance results in a non-extensive measure that effectively smears the topological stiffness of the gauge vacuum. A unified master equation for the Polyakov loop $\langle L \rangle$ is presented, governed by the thermofractal index $q$ and a single variance parameter $σ^2(T)$ that scales as $T^{1/(q-1)}$. The observed phase dynamics are shown to be asymptotic limits of this unified density: a ``soft'' algebraic growth $\langle L \rangle \propto T^{11}$ in the 1D string-like confined regime for $N_f=0$, and a rapid $1 - \langle L \rangle \propto T^{-21}$ suppression in the 3D deconfined volume for $N_f=3$. This approach provides a microscopic foundation for partial deconfinement theory and reproduces lattice QCD data with a reduced $χ^2 \approx 1.12$, offering a rigorous reconciliation between matrix model topology and the continuous QCD crossover. |
| title | QCD phase-transition under the light of Thermofractal |
| topic | High Energy Physics - Lattice High Energy Physics - Experiment High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.08735 |