k-String tensions and the 1/N expansion

Agostino Patella; Biagio Lucini; Jeff Greensite

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k-String tensions and the 1/N expansion

Jeff Greensite, Biagio Lucini, Agostino Patella

High Energy Physics - Theory · Submitted 27 Jan 2011

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

The authors' main claim We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.57 · mentions code or data availability 0.02.

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We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling.	background 0.75	0.12	0.06	unclear 0.84
s1	We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops.	result 1.00	0.95	0.81	hedged possibility 0.78
s2	It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action.	method 0.52	0.92	0.13	asserted 1.00
s3	This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions.	result 0.52	0.67	0.13	asserted 1.00
s4	Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.	result 0.49	0.90	0.08	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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Original abstract

We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.

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10 arXiv papers cite this in 16 sentences

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Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We show, however, that k-string tensions may, in fact, have leading 1/N corrections, and consistency with the large-N expansion, in the open string sector, is achieved by an exact pairwise cancellation among terms involving odd powers of 1/N in particular combinations of Wilson loops.

k-String tensions and their large-N dependence · 1.00

Papers citing it · 12 sentences without a confident label

Cites it as background 4 papers

Its tension has been vastly discussed in the literature [ref] .

k-String Tension from Eguchi-Kawai Reduction · Introduction · 1.00
For a recent discussion of $k$-string tensions in the context of the large-$N$ expansion, cf. [ref] . ] As argued in ref.

Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum · Vacuum state proposals · 0.97
The $N$-ality dependence of confining string tensions is a probe of the confinement mechanism [ref] and could be compared with studies of confining string tensions in both analytic and lattice setups [ref] .

Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow · Future Work · 0.88

What it cites · 58 sentences without a confident label

Contests 1 paper

We differ with Ref. [ref] on this point at strong coupling, and we will now argue that these states are non-degenerate at weak couplings as well.

Hot QCD, k-strings and the adjoint monopole gas model · Discussion: More on degeneracy · contest 0.79

Uses data or values from 1 paper

At present, the lattice Monte Carlo data favors $O(1/N)$ [ref] , at least for $k=2$ strings in $D=3$ dimensions.

Closed k-strings in SU(N) gauge theories : 2+1 dimensions · Conclusions · 0.84

Compares with 1 paper

Analogies and differences between our arguments and those presented in [ref] will also be discussed below.

Hot QCD, k-strings and the adjoint monopole gas model · Introduction · 0.93

Cites as background 11 papers

The fact that the same quantity, namely the correlators of Polyakov loops, can be expanded in open and closed string states is known as open-closed string duality and gives constraints on the functional form of the energy levels (see e.g. [ref] and references therein).

String excitation energies in SU(N) gauge theories beyond the free-string approximation · Open and closed strings · 0.90
Open strings are characterized by the group representation of the static sources at their ends (see e.g. [ref] ), and a degeneracy among these states, at infinite $N$, is understandable.

Degeneracy Between the Regge Slope of Mesons and Baryons from Supersymmetry · $k$-strings and large-$N$ · 0.95
Open strings are characterized by the group representation of the static sources at their ends (see e.g. [ref] ), and a degeneracy among these states, at infinite $N$, is understandable.

Quark confinement and the bosonic string · $k$-strings and large-$N$ · 0.95

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