dorsal/arxiv
View SchemaQCD phase-transition under the light of Thermofractal
| Authors | Airton Deppman |
|---|---|
| Categories | |
| ArXiv ID | 2601.08735vv1 |
| URL | https://arxiv.org/abs/2601.08735 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
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 $\beta$-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 $\sigma^2(T)$ 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 $\chi^2 \approx 1.12$, offering a rigorous reconciliation between matrix model topology and the continuous QCD crossover.
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"abstract": "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 $\\beta$-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 $\\sigma^2(T)$ that scales as $T^{1/(q-1)}$. The observed phase dynamics are shown to be asymptotic limits of this unified density: a ``soft\u0027\u0027 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 $\\chi^2 \\approx 1.12$, offering a rigorous reconciliation between matrix model topology and the continuous QCD crossover.",
"arxiv_id": "2601.08735",
"authors": [
"Airton Deppman"
],
"categories": [
"hep-lat",
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"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "QCD phase-transition under the light of Thermofractal",
"url": "https://arxiv.org/abs/2601.08735",
"version": "v1"
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