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The Chiral Symmetry Breaking/Restoration in Dyonic Vacuum
High Energy Physics - Phenomenology · Submitted 26 Jan 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim At intermediate temperatures the diluteness reaches some critical level at which chiral symmetry gets restored: we explain why it is very different for the fundamental and adjoint fermions.
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The abstract, sentence by sentence
We discuss the topological phenomena in the QCD-like theories with variable number of fundamental $N_f$ or adjoint $N_a$ fermions, focusing on the temperatures at or above the critical value $T_c$ of chiral symmetry restoration. Nonzero average of the Polyakov line, or holonomy, splits instantons into (anti)selfdual dyons, and we study both bosonic and fermionic interactions between them. The high temperature phase is a dilute gas of "molecules" made of $2N_c$ dyons, neutral in topological, electric and magnetic charges. At intermediate temperatures the diluteness reaches some critical level at which chiral symmetry gets restored: we explain why it is very different for the fundamental and adjoint fermions. At high density the ensemble is a strongly coupled liquid with crystal-like short range order: we speculate about its structure at small and large $N_f$. We finally explaine certain lattice observations and suggest a number of further lattice tests.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss the topological phenomena in the QCD-like theories with variable number of fundamental $N_f$ or adjoint $N_a$ fermions, focusing on the temperatures at or above the critical value $T_c$ of chiral symmetry restoration. | contribution 0.53 | 0.60 | 0.07 | asserted 0.76 |
| s1 | Nonzero average of the Polyakov line, or holonomy, splits instantons into (anti)selfdual dyons, and we study both bosonic and fermionic interactions between them. | contribution 0.75 | 0.67 | 0.09 | asserted 1.00 |
| s2 | The high temperature phase is a dilute gas of "molecules" made of $2N_c$ dyons, neutral in topological, electric and magnetic charges. | result 0.93 | 0.61 | 0.18 | asserted 1.00 |
| s3 | At intermediate temperatures the diluteness reaches some critical level at which chiral symmetry gets restored: we explain why it is very different for the fundamental and adjoint fermions. | result 0.66 | 0.75 | 0.42 | asserted 0.99 |
| s4 | At high density the ensemble is a strongly coupled liquid with crystal-like short range order: we speculate about its structure at small and large $N_f$. | result 0.81 | 0.40 | 0.11 | asserted 0.70 |
| s5 | We finally explaine certain lattice observations and suggest a number of further lattice tests. | future work 0.93 | 0.65 | 0.08 | asserted 0.76 |
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The paper
Original abstract
We discuss the topological phenomena in the QCD-like theories with variable number of fundamental $N_f$ or adjoint $N_a$ fermions, focusing on the temperatures at or above the critical value $T_c$ of chiral symmetry restoration. Nonzero average of the Polyakov line, or holonomy, splits instantons into (anti)selfdual dyons, and we study both bosonic and fermionic interactions between them. The high temperature phase is a dilute gas of "molecules" made of $2N_c$ dyons, neutral in topological, electric and magnetic charges. At intermediate temperatures the diluteness reaches some critical level at which chiral symmetry gets restored: we explain why it is very different for the fundamental and adjoint fermions. At high density the ensemble is a strongly coupled liquid with crystal-like short range order: we speculate about its structure at small and large $N_f$. We finally explaine certain lattice observations and suggest a number of further lattice tests.
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References
How the literature uses it
23 arXiv papers cite this in 47 sentences
Papers citing it · 33 sentences without a confident label
Uses its method or tool 1 paper
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We follow [ref] and use a simple interpolation formula [equation] where $v̅= 2πT-v$.
Instanton-dyon Ensemble with two Dynamical Quarks: the Chiral Symmetry Breaking · The hopping amplitudes · 1.00
Compares with it 2 papers
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For $μ=0$, we recover the zero modes in [ref] .
The Instanton-Dyon Liquid Model III: Finite Chemical Potential · Quark zero modes at finite $μ$ · 0.87
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We note that ([ref]) is similar but not identical to the effective potential discussed in [ref] ) using an excluded volume approach.
Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV · Effective potential with $N_f=0$ · 1.00
Cites it as support 2 papers
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The random hopping of these zero modes in the instanton-dyon liquid is at the origin of the spontaneous breaking of chiral symmetry as has been shown both numerically [ref] and using mean-field methods [ref] .
The Instanton-Dyon Liquid Model V: Twisted Light Quarks · Introduction · 0.97
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Models emulating this physical set-up also exhibit non-abelian chiral symmetry breaking [ref] .
New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence · Magnetic and Neutral Bions in QCD(adj): Confinement and Center-Stability · 0.97
Cites it as background 8 papers
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Interactions and statistical ensemble of instanton-dyons and antidyons have been studied qualitatively using neutral dyon-antidyon pairs in [ref] , recently complemented by first numerical simulations [ref] .
Holonomy potential and confinement from a simple model of the gauge topology · Introduction · 0.89
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Preliminary studies of the dyon-anti-dyon vacuum in the presence of light quarks were developed in [ref] .
The Instanton-Dyon Liquid Model III: Finite Chemical Potential · Introduction · 0.83
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Another group [ref] study instanton-dyons in the pure gauge and/or QCD-like theories. in which dyons are dilute at high temperature but form a rather dense plasma at $T∼T_c$.
Classical interactions of the instanton-dyons with antidyons · Introduction · 0.95
What it cites · 36 sentences without a confident label
Builds on 1 paper
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Since, unlike [ref] , we are interested in the theories with fermions, we introduced extra factors which include that for zero modes as well as the nonzero mode part dZ_mol = dZ_LM dZ_L̅M̅ [ m^2 +| T_IA(r_LL̅)|^2 Λ^2 ]^N_f C(N_f) ( π^2 r_LM r_L̅M̅Λ^4 T^2 )^N_f/6 e^- V_scr -V_LL̅ As discussed in the preceding section, $V_screening$ is defined by the 4-particle expression for $A_4$ integrated over the volume.
Quantum weights of dyons and of instantons with non-trivial holonomy · Statistical Mechanics of a Single Dyonic Molecule · 0.87
Uses the method or tool of 1 paper
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We use the moduli space metric $G_ij$ for the selfdual sector as suggested in [ref] to calculate the effective potential of a crystal configuration of $L$ and $M$ dyons, with a lattice spacing $a$, for a displacement of a single dyon somewhere in a center.
Topology and confinement · Statistical mechanics driven by bosonic moduli space metric effects · 0.99
Uses data or values from 4 papers
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The open diamonds in Fig.[ref](a) correspond to lattice data from Ref. [ref] : they show the critical line of the chiral restoration (thin solid line).
Chiral phase transition at finite temperature and conformal dynamics in large Nf QCD · The critical lines versus the number of fermions $N_f,N_a$ · 0.94
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Yet calculated for $N_f=4$ [ref] and $8$ [ref] theories one consistently finds about twice smaller values, and at $N_f=12$ these splittings were not observed at all [ref] .
Chiral symmetry of QCD with twelve light flavors · The magnitude of the chiral splittings versus $N_f$. · 0.84
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Yet calculated for $N_f=4$ [ref] and $8$ [ref] theories one consistently finds about twice smaller values, and at $N_f=12$ these splittings were not observed at all [ref] .
Lattice QCD with 8 and 12 degenerate quark flavors · The magnitude of the chiral splittings versus $N_f$. · 0.84
Cites as support 2 papers
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In view of the trend just discussed, as well as because of the two transition observed in [ref] , we expect the chiral and deconfinement lines to separate, perhaps already at $N_f>4$ or so.
Novel phase in SU(3) lattice gauge theory with 12 light fermions · The magnitude of the chiral splittings versus $N_f$. · 0.98
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As demonstrated in [ref] , those have $two$ topological lumps, confirming the picture of the paired instanton-antiinstantons [ref] .
Testing the self-duality of topological lumps in SU(3) lattice gauge theory · Identifying the topological objects via their fermionic zero modes. · 0.97
Cites as background 9 papers
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The interaction between the dyons due to an exchange of the adjoint fermions has been discussed by Unsal [ref] .
Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions · From instantons to dyons · 0.93
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An extensive discussion of the zero modes for the periodic and antiperiodic adjoint fermions can be found in [ref] .
Adjoint fermion zero-modes for SU(N) calorons · Fermion-induced interactions · 0.95
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In the context of the QCD-like theories, the predecessor of this paper is the so-called instanton liquid model, for a review see [ref] .
Instantons in QCD · From instantons to dyons · 0.91
Discussion
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