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Conformal window in QCD for large numbers of colours and flavours
High Energy Physics - Phenomenology · Submitted 31 Jul 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We conjecture that the phase transitions in QCD at large number of colours N\gg 1 is triggered by the drastic change in the instanton density.
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We conjecture that the phase transitions in QCD at large number of colours N\gg 1 is triggered by the drastic change in the instanton density. As a result of it, all physical observables also experience some sharp modification in the \theta behaviour. This conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at temperature T=T_c where $\theta$ dependence of the vacuum energy experiences a sudden change in behaviour: from N^2\cos(\theta/N) at T<T_c to \cos\theta\exp(-N) at T>T_c. This conjecture is also supported by recent lattice studies. We employ this conjecture to study a possible phase transition as a function of \kappa\equiv N_f/N from confinement to conformal phase in the Veneziano limit N_f\sim N when number of flavours and colours are large, but the ratio \kappa is finite. Technically, we consider an operator which gets its expectation value solely from nonperturbative instaton effects. When \kappa exceeds some critical value \kappa> \kappa_c the integral over instanton size is dominated by small-size instatons, making the instanton computations reliable with expected \exp(-N) behaviour. However, when \kappa<\kappa_c, the integral over instaton size is dominated by large-size instantons, and the instanton expansion breaks down. This regime with \kappa<\kappa_c corresponds to the confinement phase. We also compute the variation of the critical \kappa_c(T, \mu) when the temperature and chemical potential T, \mu \ll \Lambda_{QCD} slightly vary. We also discuss the scaling (x_i-x_j)^{-\gamma_{\rm det}} in the conformal phase.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We conjecture that the phase transitions in QCD at large number of colours N\gg 1 is triggered by the drastic change in the instanton density. | contribution 0.90 | 0.50 | 0.32 | speculative 1.00 |
| s1 | As a result of it, all physical observables also experience some sharp modification in the \theta behaviour. | interpretation 0.78 | 0.25 | 0.09 | asserted 0.93 |
| s2 | This conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at temperature T=T_c where $\theta$ dependence of the vacuum energy experiences a sudden change in behaviour: from N^2\cos(\theta/N) at T<T_c to \cos\theta\exp(-N) at T>T_c. | background 0.88 | 0.08 | 0.09 | asserted 0.88 |
| s3 | This conjecture is also supported by recent lattice studies. | background 0.94 | 0.05 | 0.03 | asserted 0.76 |
| s4 | We employ this conjecture to study a possible phase transition as a function of \kappa\equiv N_f/N from confinement to conformal phase in the Veneziano limit N_f\sim N when number of flavours and colours are large, but the ratio \kappa is finite. | contribution 0.97 | 0.85 | 0.11 | hedged possibility 0.74 |
| s5 | Technically, we consider an operator which gets its expectation value solely from nonperturbative instaton effects. | method 0.92 | 0.76 | 0.03 | asserted 1.00 |
| s6 | When \kappa exceeds some critical value \kappa> \kappa_c the integral over instanton size is dominated by small-size instatons, making the instanton computations reliable with expected \exp(-N) behaviour. | result 0.81 | 0.78 | 0.15 | asserted 0.99 |
| s7 | However, when \kappa<\kappa_c, the integral over instaton size is dominated by large-size instantons, and the instanton expansion breaks down. | result 0.88 | 0.79 | 0.09 | asserted 1.00 |
| s8 | This regime with \kappa<\kappa_c corresponds to the confinement phase. | interpretation 0.82 | 0.59 | 0.13 | asserted 1.00 |
| s9 | We also compute the variation of the critical \kappa_c(T, \mu) when the temperature and chemical potential T, \mu \ll \Lambda_{QCD} slightly vary. | result 0.57 | 0.93 | 0.06 | asserted 0.99 |
| s10 | We also discuss the scaling (x_i-x_j)^{-\gamma_{\rm det}} in the conformal phase. | result 0.66 | 0.82 | 0.07 | asserted 0.84 |
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The paper
Original abstract
We conjecture that the phase transitions in QCD at large number of colours N\gg 1 is triggered by the drastic change in the instanton density. As a result of it, all physical observables also experience some sharp modification in the \theta behaviour. This conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at temperature T=T_c where $\theta$ dependence of the vacuum energy experiences a sudden change in behaviour: from N^2\cos(\theta/N) at T<T_c to \cos\theta\exp(-N) at T>T_c. This conjecture is also supported by recent lattice studies. We employ this conjecture to study a possible phase transition as a function of \kappa\equiv N_f/N from confinement to conformal phase in the Veneziano limit N_f\sim N when number of flavours and colours are large, but the ratio \kappa is finite. Technically, we consider an operator which gets its expectation value solely from nonperturbative instaton effects. When \kappa exceeds some critical value \kappa> \kappa_c the integral over instanton size is dominated by small-size instatons, making the instanton computations reliable with expected \exp(-N) behaviour. However, when \kappa<\kappa_c, the integral over instaton size is dominated by large-size instantons, and the instanton expansion breaks down. This regime with \kappa<\kappa_c corresponds to the confinement phase. We also compute the variation of the critical \kappa_c(T, \mu) when the temperature and chemical potential T, \mu \ll \Lambda_{QCD} slightly vary. We also discuss the scaling (x_i-x_j)^{-\gamma_{\rm det}} in the conformal phase.
Human review
References
How the literature uses it
5 arXiv papers cite this in 8 sentences
What it cites · 59 sentences without a confident label
Builds on 1 paper
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The same guiding principle can be applied for studying the dense matter as well [ref] .
Confinement- Deconfinement Phase Transition in Hot and Dense QCD at Large N · Confinement- Deconfinement Phase Transition in hot and dense QCD at large $N$. · 0.80
Uses the method or tool of 2 papers
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Γ(N+1)=√(2πN)N^N e^-N(1+1/12N +O(1/N^2)) One follows the same procedure as before [ref] to evaluate integral $∫dρ$ and take the limit $N→∞$ at the end of computation.
Confinement- Deconfinement Phase Transition in Hot and Dense QCD at Large N · Computations and technical details · 0.94
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Γ(N+1)=√(2πN)N^N e^-N(1+1/12N +O(1/N^2)) One follows the same procedure as before [ref] to evaluate integral $∫dρ$ and take the limit $N→∞$ at the end of computation.
Phase Transitions, theta Behavior and Instantons in QCD and its Holographic Model · Computations and technical details · 0.94
Uses data or values from 1 paper
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If, instead, we adopt $κ_c≃4$ as suggested by the lattice simulations at $N=3$, see review paper [ref] , we infer that $M/Λ$ should be $M/Λ ≃1.55$ in eq.
Strongly and slightly flavored gauge theories · Computations and technical details · 0.92
Cites as support 5 papers
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First of all, this criteria is motivated by the observation that in holographic model of QCD the confinement -deconfinement phase transition indeed happens precisely at the temperature $T=T_c$ where $θ$ dependence experiences a sudden change in behaviour, see [ref] and many related references therein.
Phase Transitions, theta Behavior and Instantons in QCD and its Holographic Model · Introduction · 1.00
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First of all, this criteria is motivated by the observation that in holographic model of QCD the confinement -deconfinement phase transition indeed happens precisely at the temperature $T=T_c$ where $θ$ dependence experiences a sudden change in behaviour, see [ref] and many related references therein.
On Classification of QCD defects via holography · Introduction · 1.00
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Secondly, the proposal is supported by the numerical lattice results [ref] - [ref] , see also a review article [ref] , which unambiguously suggest that the topological fluctuations related to $θ$ (in particular the topological susceptibility) are strongly suppressed in deconfined phase, and this suppression becomes more severe with increasing $N$.
Theta dependence of SU(N) gauge theories in the presence of a topological term · Introduction · 1.00
Cites as background 18 papers
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At zero temperature the confined phase is expected to be replaced by a “non- Abelian Coulomb phase", conventionally referred to as the “conformal window", see some original analytical results [ref] , the recent lattice computations [ref] and review [ref] on the subject.
Twelve massless flavors and three colors below the conformal window · Introduction · 0.99
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At zero temperature the confined phase is expected to be replaced by a “non- Abelian Coulomb phase", conventionally referred to as the “conformal window", see some original analytical results [ref] , the recent lattice computations [ref] and review [ref] on the subject.
Lattice Simulations and Infrared Conformality · Introduction · 0.99
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At zero temperature the confined phase is expected to be replaced by a “non- Abelian Coulomb phase", conventionally referred to as the “conformal window", see some original analytical results [ref] , the recent lattice computations [ref] and review [ref] on the subject.
Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World · Introduction · 0.99
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