The finite-temperature chiral transition in QCD with adjoint fermions

Andrea Pelissetto; Ettore Vicari; Francesco Basile

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The finite-temperature chiral transition in QCD with adjoint fermions

Francesco Basile, Andrea Pelissetto, Ettore Vicari

High Energy Physics - Theory · Submitted 2 Dec 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class.

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arXiv IDhep-th/0412026 (version 1)

Pith IDFOR44JQY, Pith's permanent record of this paper and its review

CitationAndrea Pelissetto, Ettore Vicari, Francesco Basile. "The finite-temperature chiral transition in QCD with adjoint fermions." arXiv:hep-th/0412026 (2004). https://pith.science/paper/FOR44JQY

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.66 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.89 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the adjoint representation (aQCD). Renormalization-group arguments show that the transition can be continuous if a stable fixed point exists in the renormalization-group flow of the corresponding three-dimensional Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by exploiting two three-dimensional perturbative approaches, the massless minimal-subtraction scheme without epsilon expansion and a massive scheme in which correlation functions are renormalized at zero momentum. We compute the renormalization-group functions in the two schemes to five and six loops respectively, and determine their large-order behavior. The analyses of the series show the presence of a stable three-dimensional fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This fixed point does not appear in an epsilon-expansion analysis and therefore does not exist close to four dimensions. The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may show a more complex phase diagram with two phase transitions. One of them, if continuous, should belong to the O(3) vector universality class.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the adjoint representation (aQCD).	contribution 0.90	0.87	0.03	asserted 0.53
s1	Renormalization-group arguments show that the transition can be continuous if a stable fixed point exists in the renormalization-group flow of the corresponding three-dimensional Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and symmetry-breaking pattern SU(2N_f)->SO(2N_f).	background 0.98	0.17	0.09	hedged possibility 0.75
s2	This issue is investigated by exploiting two three-dimensional perturbative approaches, the massless minimal-subtraction scheme without epsilon expansion and a massive scheme in which correlation functions are renormalized at zero momentum.	method 0.99	0.72	0.02	asserted 0.97
s3	We compute the renormalization-group functions in the two schemes to five and six loops respectively, and determine their large-order behavior.	method 0.84	0.96	0.03	asserted 1.00
s4	The analyses of the series show the presence of a stable three-dimensional fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4).	result 1.00	0.92	0.48	asserted 1.00
s5	This fixed point does not appear in an epsilon-expansion analysis and therefore does not exist close to four dimensions.	result 0.55	0.54	0.08	asserted 1.00
s6	The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class.	interpretation 0.85	0.79	0.80	hedged possibility 0.60
s7	One-flavor aQCD may show a more complex phase diagram with two phase transitions.	result 0.65	0.41	0.04	hedged possibility 1.00
s8	One of them, if continuous, should belong to the O(3) vector universality class.	interpretation 0.53	0.35	0.04	hedged possibility 0.91

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.50.

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The paper

Original abstract

We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the adjoint representation (aQCD). Renormalization-group arguments show that the transition can be continuous if a stable fixed point exists in the renormalization-group flow of the corresponding three-dimensional Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by exploiting two three-dimensional perturbative approaches, the massless minimal-subtraction scheme without epsilon expansion and a massive scheme in which correlation functions are renormalized at zero momentum. We compute the renormalization-group functions in the two schemes to five and six loops respectively, and determine their large-order behavior. The analyses of the series show the presence of a stable three-dimensional fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This fixed point does not appear in an epsilon-expansion analysis and therefore does not exist close to four dimensions. The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may show a more complex phase diagram with two phase transitions. One of them, if continuous, should belong to the O(3) vector universality class.

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References

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Adjoint QCD on $\mathbb{R}^3\times S^1$ with twisted fermionic boundary conditions
hep-ph 2014-05 conditional novelty 6.0 of 10

Adjoint QCD on a compact space with twisted fermion boundary conditions has a rich phase structure in which bion-induced confinement is exponentially suppressed at nonzero twist and a deconfined phase can intervene be...
Change of theta dependence in 4D SU(N) gauge theories across the deconfinement transition
hep-lat 2013-01 conditional novelty 6.0 of 10

The theta dependence of 4D SU(N) gauge theory switches from a theta/N large-N scaling below the deconfinement transition to a theta-only instanton-gas form above it.
Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature
hep-lat 2012-09 conditional novelty 6.0 of 10

In the chiral symmetric phase of 2-flavor QCD, the Dirac eigenvalue density must vanish at least cubically near the origin, and the axial U(1) anomaly leaves no trace in scalar and pseudoscalar susceptibilities.
Theta dependence of SU(N) gauge theories in the presence of a topological term
hep-th 2008-03 accept novelty 2.0 of 10

Lattice measurements of the topological susceptibility and its theta-expansion coefficients in SU(N) gauge theory agree with large-N scaling and the Witten-Veneziano explanation of the U(1)_A problem.

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8 arXiv papers cite this in 20 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 17 sentences without a confident label

Compares with it 1 paper

These conditions are the same as what is found in analyses of the single-irrep subsectors of the potential [ref] , and so irrep coupling does not seem to affect which $χ$SB pattern is realized.

Stability Analysis of the Chiral Transition in SU(4) Gauge Theory with Fermions in Multiple Representations · Constraints due to Vacuum Stability and $χ$SB Pattern · 0.83

Cites it as background 2 papers

In Sec. [ref], we review the results of the calculation for the single-irrep subsectors of the theory, which have been examined previously [ref] and whose fixed points span a subset of the fixed points of the full theory (see Sec. [ref] for discussion).

Stability Analysis of the Chiral Transition in SU(4) Gauge Theory with Fermions in Multiple Representations · Introduction · 0.82
This implies that, in the case of a continuous chiral transition (note however that the transition may be also first order independently of the symmetry breaking), the critical behavior belongs to different 3D universality classes in the two cases [ref] .

Theta dependence of 4D SU(N) gauge theories at finite temperature · Introduction · 0.84

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