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Towards a semi-classical description of QCD vacuum around $T_c$
High Energy Physics - Lattice · Submitted 19 Dec 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Surprisingly, it emerges out from this study that a semi-classical description of the fermionic zero modes in the QCD vacuum is quite accurate just above $T_c$.
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The abstract, sentence by sentence
We study the vacuum topology of 2+1 flavor QCD above the chiral crossover transition, at $T \lesssim 1.2~T_c$, on lattices of size $32^3\times 8$. Since overlap fermions have exact chiral symmetry and an index theorem even on a finite lattice, we use them to detect the topological content of gauge fields generated using domain wall fermion discretization for quarks. We further use different periodicity phases along the temporal direction for the valence overlap quarks, which allows us to probe different topological structures present in the gauge field ensembles, through its zero modes. This procedure provides strong evidences that fermion zero-modes can be quantitatively understood to arise due to different species of instanton-dyons. We estimate their relative abundances from the Dirac-eigenvalue density and resolve the so called "topological clusters" via multi-parameter fits to their density, providing therefore an understanding of the interactions between instanton-dyons. The typical separation between dyons we obtain, is $\sim 0.3$ fm. Surprisingly, it emerges out from this study that a semi-classical description of the fermionic zero modes in the QCD vacuum is quite accurate just above $T_c$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the vacuum topology of 2+1 flavor QCD above the chiral crossover transition, at $T \lesssim 1.2~T_c$, on lattices of size $32^3\times 8$. | contribution 0.81 | 0.95 | 0.03 | asserted 0.89 |
| s1 | Since overlap fermions have exact chiral symmetry and an index theorem even on a finite lattice, we use them to detect the topological content of gauge fields generated using domain wall fermion discretization for quarks. | method 0.99 | 0.80 | 0.02 | asserted 0.98 |
| s2 | We further use different periodicity phases along the temporal direction for the valence overlap quarks, which allows us to probe different topological structures present in the gauge field ensembles, through its zero modes. | method 0.99 | 0.94 | 0.03 | asserted 0.94 |
| s3 | This procedure provides strong evidences that fermion zero-modes can be quantitatively understood to arise due to different species of instanton-dyons. | interpretation 0.50 | 0.90 | 0.24 | asserted 0.88 |
| s4 | We estimate their relative abundances from the Dirac-eigenvalue density and resolve the so called "topological clusters" via multi-parameter fits to their density, providing therefore an understanding of the interactions between instanton-dyons. | method 0.40 | 0.96 | 0.09 | asserted 1.00 |
| s5 | The typical separation between dyons we obtain, is $\sim 0.3$ fm. | result 1.00 | 0.96 | 0.04 | asserted 1.00 |
| s6 | Surprisingly, it emerges out from this study that a semi-classical description of the fermionic zero modes in the QCD vacuum is quite accurate just above $T_c$. | interpretation 0.82 | 0.92 | 0.85 | asserted 0.97 |
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The paper
Original abstract
We study the vacuum topology of 2+1 flavor QCD above the chiral crossover transition, at $T \lesssim 1.2~T_c$, on lattices of size $32^3\times 8$. Since overlap fermions have exact chiral symmetry and an index theorem even on a finite lattice, we use them to detect the topological content of gauge fields generated using domain wall fermion discretization for quarks. We further use different periodicity phases along the temporal direction for the valence overlap quarks, which allows us to probe different topological structures present in the gauge field ensembles, through its zero modes. This procedure provides strong evidences that fermion zero-modes can be quantitatively understood to arise due to different species of instanton-dyons. We estimate their relative abundances from the Dirac-eigenvalue density and resolve the so called "topological clusters" via multi-parameter fits to their density, providing therefore an understanding of the interactions between instanton-dyons. The typical separation between dyons we obtain, is $\sim 0.3$ fm. Surprisingly, it emerges out from this study that a semi-classical description of the fermionic zero modes in the QCD vacuum is quite accurate just above $T_c$.
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References
How the literature uses it
8 arXiv papers cite this in 16 sentences
Papers citing it · 10 sentences without a confident label
Uses its method or tool 2 papers
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We can then identify different species of instanton-dyons with the Dirac zero modes corresponding to the phases $ϕ$, following the procedure outlined in [ref] .
Correlating confinement to topological fluctuations near the crossover transition in QCD · Methodology · 1.00
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To identify instanton-dyons on the lattice, overlap fermions may be used as probes [ref] .
Confinement in non-Abelian lattice gauge theory via persistent homology · Introduction · 0.82
Cites it as support 2 papers
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In the regime $T≳T_pc$ there are regions of strong fluctuations in the local values of Polyakov loop which has been demonstrated to be anti-correlated with the probability density for the occurrence of instanton-dyons [ref] which form a semi-classical gas [ref] .
Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature · Understanding the origin of disorder and (de)localization in QCD Dirac eigenstates · 0.96
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This is motivated from the fact that the average values of the Polyakov loop at these temperatures have been shown previously to be quite accurately explained due to weakly interacting semiclassical gas of instanton-dyons [ref] .
Correlating confinement to topological fluctuations near the crossover transition in QCD · Are topological fluctuations in QCD above $T_c$ correlated to confinement? · 0.99
Cites it as background 2 papers
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The microscopic behaviour of the plasma close to phase transition, its interpretation in terms of physical degrees of freedom, including topological structures, is of course a subject of active research [ref] .
Topology and axions in QCD · Topology and the Strong CP problem · 0.95
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There are several papers relating the properties of the theory (mostly QCD) just above the critical temperature with caloron structures (see for example Ref. [ref] ).
On the fractional instanton liquid picture of the Yang-Mills vacuum and Confinement · Recent and ongoing progress · 0.97
What it cites · 12 sentences without a confident label
Builds on 1 paper
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Continuing forward from our preliminary findings reported in Ref. [ref] , we describe here our findings in a more extensive form, with several new results.
The topological objects near the chiral crossover transition in QCD · Introduction · 0.92
Uses the method or tool of 1 paper
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One way to do so is by using over-improved cooling technique [ref] .
Topology across the finite temperature transition studied by overimproved cooling in gluodynamics and QCD · Introduction · 0.97
Uses data or values from 1 paper
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The chiral crossover transition temperature was recently quantified to an unprecedented accuracy [ref] and is $T_c=156.5±1.5$ MeV.
Chiral crossover in QCD at zero and non-zero chemical potentials · Introduction · 0.99
Compares with 2 papers
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The final values at each temperature obtained from the fits, agrees quite well with the continuum estimates of the Polyakov loop obtained from independent lattice studies [ref] , shown as a gray band in the same Figure.
Polyakov loop in 2+1 flavor QCD from low to high temperatures · Multi-parameter fits of the topological clusters · 0.98
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The final values at each temperature obtained from the fits, agrees quite well with the continuum estimates of the Polyakov loop obtained from independent lattice studies [ref] , shown as a gray band in the same Figure.
Color screening in (2+1)-flavor QCD · Multi-parameter fits of the topological clusters · 0.98
Cites as background 7 papers
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Thermodynamic ensembles of dyons were studied analytically [ref] via mean-field approximation, as well as numerically [ref] .
Confining Dyon-Anti-Dyon Coulomb Liquid Model I · Introduction · 0.88
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Thermodynamic ensembles of dyons were studied analytically [ref] via mean-field approximation, as well as numerically [ref] .
Light Quarks in the Screened Dyon-Anti-Dyon Coulomb Liquid Model II · Introduction · 0.88
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Thermodynamic ensembles of dyons were studied analytically [ref] via mean-field approximation, as well as numerically [ref] .
Interacting Ensemble of the Instanton-dyons and Deconfinement Phase Transition in the SU(2) Gauge Theory · Introduction · 0.88
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