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Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
High Energy Physics - Lattice · Submitted 20 Jul 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using the exact same renormalization scheme as the previous study, we show that no fixed point of the $\beta$-function exists in the reported interval.
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The abstract, sentence by sentence
We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the SU(3) color gauge group, an infrared fixed point of the $\beta$-function was recently reported in the theory (Cheng:2014jba) with uncertainty in the location of the critical gauge coupling inside the narrow $[ 6.0<g_*^2<6.4]$ interval and widely accepted since as the strongest evidence for a conformal fixed point and scale invariance in the theory with model-building implications. Using the exact same renormalization scheme as the previous study, we show that no fixed point of the $\beta$-function exists in the reported interval. Our findings eliminate the only seemingly credible evidence for conformal fixed point and scale invariance in the $N_f=12$ model whose infrared properties remain unresolved. The implications of the recently completed 5-loop QCD beta function for arbitrary flavor number are discussed with respect to our work.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. | contribution 0.58 | 0.73 | 0.04 | asserted 0.95 |
| s1 | With twelve massless fermions in the fundamental representation of the SU(3) color gauge group, an infrared fixed point of the $\beta$-function was recently reported in the theory (Cheng:2014jba) with uncertainty in the location of the critical gauge coupling inside the narrow $[ 6.0<g_*^2<6.4]$ interval and widely accepted since as the strongest evidence for a conformal fixed point and scale invariance in the theory with model-building implications. | background 1.00 | 0.04 | 0.04 | asserted 0.96 |
| s2 | Using the exact same renormalization scheme as the previous study, we show that no fixed point of the $\beta$-function exists in the reported interval. | result 0.99 | 0.96 | 0.85 | asserted 1.00 |
| s3 | Our findings eliminate the only seemingly credible evidence for conformal fixed point and scale invariance in the $N_f=12$ model whose infrared properties remain unresolved. | interpretation 0.98 | 0.90 | 0.68 | asserted 1.00 |
| s4 | The implications of the recently completed 5-loop QCD beta function for arbitrary flavor number are discussed with respect to our work. | contribution 0.53 | 0.34 | 0.03 | unclear 0.74 |
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The paper
Original abstract
We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the SU(3) color gauge group, an infrared fixed point of the $\beta$-function was recently reported in the theory (Cheng:2014jba) with uncertainty in the location of the critical gauge coupling inside the narrow $[ 6.0<g_*^2<6.4]$ interval and widely accepted since as the strongest evidence for a conformal fixed point and scale invariance in the theory with model-building implications. Using the exact same renormalization scheme as the previous study, we show that no fixed point of the $\beta$-function exists in the reported interval. Our findings eliminate the only seemingly credible evidence for conformal fixed point and scale invariance in the $N_f=12$ model whose infrared properties remain unresolved. The implications of the recently completed 5-loop QCD beta function for arbitrary flavor number are discussed with respect to our work.
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References
How the literature uses it
30 arXiv papers cite this in 66 sentences
Papers whose main result relates to this one's
States a conflicting result 4 papers
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From the step-scaling analysis, we find that the infrared behavior of the theory is governed by a non-trivial fixed point.
Conformal fixed point of SU(3) gauge theory with 12 fundamental fermions · 1.00
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We observe an IR fixed point at $g_{\star}^2 = 7.3\left(_{-2}^{+8}\right)$ in the $c = \sqrt{8t} / L = 0.25$ scheme, and $g_{\star}^2 = 7.3\left(_{-3}^{+6}\right)$ with c=0.3, combining statistical and systematic uncertainties in quadrature.
Nonperturbative beta function of twelve-flavor SU(3) gauge theory · 1.00
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In the case of the twelve flavor system, our $O(a^2)$ Symanzik improved set-up predicts a conformal infrared fixed point around $g_c^2 \sim 5.5$ in the $c=0.25$ scheme, which is presently in tension with staggered fermion results in the literature.
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We present strong numerical evidence for the existence of an infrared fixed point in the renormalization group flow of the SU(3) gauge-fermion system with twelve massless fermions in the fundamental representation.
Infrared fixed point in the massless twelve-flavor SU(3) gauge-fermion system · 1.00
Papers citing it · 34 sentences without a confident label
Contests it 2 papers
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In disagreement with [ref] , the IRFP was refuted in [ref] .
Extended investigation of the twelve-flavor $\beta$-function · History of the IRFP with 12 massless fermions · contest 0.84
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As explained in 2) of Sec. [ref], despite the limit $L→∞$ of $σ(s,L)$ is taken in [ref] , the finite volume corrections in $σ(s,L)$ are not removed since $c>0$ is held fixed.
On the gradient flow of the Lagrangian density in non-Abelian gauge theories · Lattice results · contest 0.75
Uses its method or tool 2 papers
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Precision tuning of the bare gauge coupling $6/g^2_0$ was used exclusively for each step calculation in [ref] using the $c=0.20$ renormalization scheme with $s=2$ step size.
Extended investigation of the twelve-flavor $\beta$-function · SSC gradient flow with c=0.20 renormalization scheme · 0.96
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The Markov Chain Monte Carlo (MCMC) based gauge field generation of the lattice ensembles use the Rational Hybrid Monte Carlo (RHMC) evolution code as described in [ref] together with further details on the lattice implementation of the step $β$-function and its continuum limit.
From ten-flavor tests of the $\beta$-function to $\alpha_s$ at the Z-pole · The ten-flavor lattice ensembles of our analysis · 0.99
Uses its data or values 1 paper
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The $N_f=12$ theory is likely in the conformal window (with $g_*^2=6.2(2)$ [ref] ) .
Chiral symmetry breaking and confinement: separating the scales · Results and Outlook for One Representation SU$(N)$ · 0.85
Compares with it 4 papers
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The results of lattice studies are controversial as Ref. [ref] finds a FP in the gradient flow $c=0.25$ scheme at $g^2≈7.3$, while Refs. [ref] do not observe any sign of a FP.
Gradient flow step-scaling function for SU(3) with twelve flavors · Introduction · 0.92
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In addition to the perturbative $MS$ predictions we also show the results obtained with staggered fermions from Ref. [ref] and Refs. [ref] .
Nonperturbative determination of $\beta$ functions for SU(3) gauge theories with 10 and 12 fundamental flavors using domain wall fermions · Discussion · 0.96
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[ref] and [ref] .
Nonperturbative beta function of twelve-flavor SU(3) gauge theory · Gradient flow step scaling and its improvement · 0.81
Cites it as support 2 papers
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This assumption has substantial numerical support [ref] and remaining concerns [ref] were recently addressed in Ref. [ref] .
Infrared properties of a prototype model for beyond-Standard Model physics · Hyperscaling · 0.98
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The accumulating evidence for an IR fixed point in the discrete function [ref] , in addition to further supporting evidence (summarized in sec:intro) from the phase diagram at zero and finite temperature [ref] as well as hyperscaling of the hadron masses and decay constants [ref] increases our confidence in the conclusion that the 12-flavor system is conformal in the IR.
Nonperturbative beta function of twelve-flavor SU(3) gauge theory · Discussion and conclusions · 1.00
Cites it as background 11 papers
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There are several nonperturbative lattice calculations that explore the infrared properties of this system [ref] .
Determination of the $N_f=12$ step scaling function using M\"obius domain wall fermions · Introduction · 0.99
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So far only calculations based on staggered fermions have been performed [ref] .
Gradient flow step-scaling function for SU(3) with twelve flavors · Conclusion · 0.86
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Such techniques include perturbation theory [ref] , use of the gap equation [ref] , functional renormalization group methods [ref] , conformal expansion [ref] , conformal bootstrap [ref] , the background field method [ref] , perturbative non-relativistic quantum chromodynamics [ref] , large-$N$ expansion [ref] , and nonperturbative lattice simulations [ref] .
Infrared fixed point in the massless twelve-flavor SU(3) gauge-fermion system · Introduction · 0.85
What it cites · 20 sentences without a confident label
Contests 1 paper
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The final results of our continuum step $β$-function are shown in Figure [ref] with overwhelming statistical evidence against the IRFP of [ref] in the targeted interval.
Improving the continuum limit of gradient flow step scaling · Introduction · contest 0.88
Uses the method or tool of 5 papers
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Following [ref] , we define the one-parameter family of renormalized non-perturbative gauge couplings for strongly coupled gauge theories built on the SU(N) color group with $N_f$ massless dynamical fermions,
The Yang-Mills gradient flow in finite volume · Introduction · 0.93
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Following [ref] , we define the one-parameter family of renormalized non-perturbative gauge couplings for strongly coupled gauge theories built on the SU(N) color group with $N_f$ massless dynamical fermions,
The gradient flow running coupling scheme · Introduction · 0.93
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The algorithmic details of our new $N_f=12$ simulations are similar to [ref] .
The running coupling of 8 flavors and 3 colors · Introduction · 0.97
Compares with 2 papers
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The 4-loop $MS$ result only slightly shifts the prediction and is closer to [ref] .
Improving the continuum limit of gradient flow step scaling · Introduction · 0.88
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Comparing near-conformal models, with details explained in Figure [ref], a light composite scalar of the massless SU(2) flavor doublet in the sextet fermion representation of SU(3) color was reported in [ref] whereas the $N_f=8$ light scalar with fermions in the fundamental representation was discovered in [ref] and confirmed recently [ref] .
Strongly interacting dynamics and the search for new physics at the LHC · Introduction · 0.80
Cites as background 5 papers
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In a significant new development, the first $MS$ calculation of the 5-loop $β$-function was completed for arbitrary flavor number in QCD [ref] .
Five-Loop Running of the QCD coupling constant · Introduction · 0.91
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The slope of the $β$-function at the fixed point is a scheme-independent scaling exponent $ω$ which controls the leading conformal scaling corrections to fermion mass deformations close to the IRFP [ref] .
The infrared dynamics of Minimal Walking Technicolor · Introduction · 0.99
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The slope of the $β$-function at the fixed point is a scheme-independent scaling exponent $ω$ which controls the leading conformal scaling corrections to fermion mass deformations close to the IRFP [ref] .
Hyperscaling relations in mass-deformed conformal gauge theories · Introduction · 0.99
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