Constrained effective potential in hot QCD

C.P.Korthals Altes

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Constrained effective potential in hot QCD

C.P.Korthals Altes

High Energy Physics - Theory · Submitted 29 Oct 1993

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

The authors' main claim It also follows, that absolute minima of the potential are at the centergroup values of the loop.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.15 · mentions code or data availability 0.02.

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Constrained effective potentials in hot gauge theory give the probability that a configuration p of the order parameter (Polyakov loop) occurs. They are important in the analysis of surface effects and bubble formation in the plasma. The vector potential appears non-linearly in the loop; in weak coupling the linear term gives rise to the traditional free energy graphs. But the non-linear terms generate insertions of the constrained modes into the free energy graphs, through renormalisations of the Polyakov loop. These insertions are gauge dependent and are necessary to cancel the gauge dependence of the free energy graphs. The latter is shown, through the BRST identities, to have again the form of constrained mode insertions. It also follows, that absolute minima of the potential are at the centergroup values of the loop. We evaluate the two-loop contributions for SU(N) gauge theories, with and without quarks, for the full domain of the N-1 variables.

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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	Constrained effective potentials in hot gauge theory give the probability that a configuration p of the order parameter (Polyakov loop) occurs.	background 1.00	0.09	0.07	asserted 1.00
s1	They are important in the analysis of surface effects and bubble formation in the plasma.	background 0.99	0.06	0.04	asserted 1.00
s2	The vector potential appears non-linearly in the loop; in weak coupling the linear term gives rise to the traditional free energy graphs.	background 0.92	0.15	0.04	asserted 0.99
s3	But the non-linear terms generate insertions of the constrained modes into the free energy graphs, through renormalisations of the Polyakov loop.	result 0.46	0.42	0.10	asserted 1.00
s4	These insertions are gauge dependent and are necessary to cancel the gauge dependence of the free energy graphs.	result 0.54	0.46	0.13	asserted 1.00
s5	The latter is shown, through the BRST identities, to have again the form of constrained mode insertions.	result 0.75	0.68	0.10	asserted 1.00
s6	It also follows, that absolute minima of the potential are at the centergroup values of the loop.	result 0.90	0.58	0.22	asserted 1.00
s7	We evaluate the two-loop contributions for SU(N) gauge theories, with and without quarks, for the full domain of the N-1 variables.	contribution 0.93	0.95	0.12	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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Original abstract

Constrained effective potentials in hot gauge theory give the probability that a configuration p of the order parameter (Polyakov loop) occurs. They are important in the analysis of surface effects and bubble formation in the plasma. The vector potential appears non-linearly in the loop; in weak coupling the linear term gives rise to the traditional free energy graphs. But the non-linear terms generate insertions of the constrained modes into the free energy graphs, through renormalisations of the Polyakov loop. These insertions are gauge dependent and are necessary to cancel the gauge dependence of the free energy graphs. The latter is shown, through the BRST identities, to have again the form of constrained mode insertions. It also follows, that absolute minima of the potential are at the centergroup values of the loop. We evaluate the two-loop contributions for SU(N) gauge theories, with and without quarks, for the full domain of the N-1 variables.

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References

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Cited by 6 Pith papers

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

The Great Wall of the Standard Model
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Deconfining Phase Transition under Real Rotation: A Matrix Model Study
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A matrix model extended to rotating gluon plasma shows the deconfining temperature decreases with rotation and radial distance, with non-monotonic behavior possible if the effective mass is rotation-dependent.
Continuity, Deconfinement, and (Super) Yang-Mills Theory
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In softly broken N=1 super Yang-Mills on R^3 x S^1 the center-symmetry-changing transition is semiclassically computable and second order, and the same monopole-instanton versus neutral-bion competition is argued to d...
Effective matrix model for deconfinement in pure gauge theories
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A two-parameter matrix model fitted to lattice pressure and latent heat reproduces the 't Hooft loop and explains the first-order deconfinement transition for all N of three or more.
Imaginary Rotating Gluonic Matter at Strong Coupling
hep-ph 2025-06 conditional novelty 5.0 of 10

At strong coupling, imaginary rotation suppresses the Polyakov-loop interaction, so the predicted deconfinement temperature of pure gluonic matter increases with the imaginary angular velocity.

Show 1 more citing papers

Polyakov loop modeling for hot QCD
hep-ph 2017-05 accept novelty 1.0 of 10

The review organizes the Polyakov loop as an approximate deconfinement order parameter and as a building block for hot-QCD models.

How the literature uses it

22 arXiv papers cite this in 55 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 · 35 sentences without a confident label

Builds on it 2 papers

To this end, we generalize earlier thermal studies of Refs. [ref] and [ref] to incorporate flavor-holonomy.

Quantum distillation in QCD · Gauge holonomy potentials without and with flavor holonomy twists · 0.99
We calculate the gauge-holonomy potential for the Polyakov loop: [equation] at two-loop order with the boundary conditions [ref].[Two-loop order suffices to determine the realization of CFC-symmetry for any flavor-holonomy background.] To do so, we generalized the tour de force thermal studies of Refs. [ref] and [ref] to incorporate flavor-holonomy backgrounds.

Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD · Color-holonomy potentials in the flavor-holonomy background and surprises · 0.98

Uses its method or tool 2 papers

In order to achieve this, we use a common trick to construct the so-called constrained effective potential [ref] introducing a delta function as [equation] Replacing the order of integration and using the Fourier representation for the delta function we obtain, [equation] Now the group integration simplifies with the Haar measure or the Vandermonde determinant taken into account explicitly, leading to [equation] and then the partition function after the $ω$ and the $γ$ integrations should read, [equation] with the effective potential defined by [equation] From this expression it is clear that $V_Vdm(ℓ)$, the explicit form of which we will discuss soon later, corresponds to $-lnH$ we have encountered in the strong coupling calculation in Sec. [ref].

Polyakov loop modeling for hot QCD · Effective matrix theory · 0.99
The insertion method is a straightforward expansion of the gauge action and the constraint in terms of the fluctuation fields $A_μ$ and $ϵ^qu$ [ref] .

Free energy of a Holonomous Plasma · Insertion method · 0.92

Compares with it 2 papers

We note firstly that the parametric dependence on the gauge coupling is the same as in ordinary Yang-Mills theory [ref] .

Z(N) Domain walls in hot N=4 SYM at weak and strong coupling · Full one-loop effective action · 0.88
This agrees with previous results, such as Eq. (3.12) of [ref] .

Free energy of a Holonomous Plasma · Expansion of Polyakov loops to quadratic order · 0.98

Cites it as background 10 papers

Without rotation, the perturbative Polyakov loop potential, known as the GPY-Weiss potential [ref] , spontaneously breaks center symmetry, which is consistent with deconfinement expected at high temperature; for a review, see Ref. [ref] .

Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity · Introduction · 0.95
As first established in the works of [ref] , the explicit profiles of the $ℤ_N$ interfaces and their tensions can be computed at weak coupling, utilizing high temperature perturbative and semiclassical methods.

Z(N) Domain walls in hot N=4 SYM at weak and strong coupling · Preliminaries · 0.80
To treat such a holonomous plasma, it is most natural to take a constant, background field for the vector potential, $_0 ∼Θ T/g$, where $Θ$ is a diagonal, traceless color matrix [ref] .

Free energy of a Holonomous Plasma · Introduction · 0.84

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