Confinement on $\mathbb{R}^3 \times \mathbb{S}^1$ and Double-String Collapse

Erich Poppitz; Mathew W. Bub; Samuel S. Y. Wong

RECORD

Confinement on $\mathbb{R}^3 \times \mathbb{S}^1$ and Double-String Collapse

Mathew W. Bub, Erich Poppitz, Samuel S. Y. Wong

High Energy Physics - Theory · Submitted 9 Oct 2020

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

The authors' main claim We numerically study this mechanism and find that double-string confinement holds for strings of all $N$-alities, except for those between fundamental quarks.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID2010.04330 (version 2)

Pith IDQ2O4AC36, Pith's permanent record of this paper and its review

CitationErich Poppitz, Mathew W. Bub, Samuel S. Y. Wong. "Confinement on $\mathbb{R}^3 \times \mathbb{S}^1$ and Double-String Collapse." arXiv:2010.04330 (2020). https://pith.science/paper/Q2O4AC36

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,451 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.56 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study confining strings in ${\cal{N}}=1$ supersymmetric $SU(N_c)$ Yang-Mills theory in the semiclassical regime on $\mathbb{R}^{1,2} \times \mathbb{S}^1$. Static quarks are expected to be confined by double strings composed of two domain walls - which are lines in $\mathbb{R}^2$ - rather than by a single flux tube. Each domain wall carries part of the quarks' chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all $N$-alities, except for those between fundamental quarks. We show that, for $N_c \ge 5$, the two domain walls confining unit $N$-ality quarks attract and form non-BPS bound states, collapsing to a single flux line. We determine the $N$-ality dependence of the string tensions for $2 \le N_c \le 10$. Compared to known scaling laws, we find a weaker, almost flat $N$-ality dependence, which is qualitatively explained by the properties of BPS domain walls. We also quantitatively study the behavior of confining strings upon increasing the $\mathbb{S}^1$ size by including the effect of virtual "$W$-bosons" and show that the qualitative features of double-string confinement persist.

background contribution method result interpretation main claim

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 confining strings in ${\cal{N}}=1$ supersymmetric $SU(N_c)$ Yang-Mills theory in the semiclassical regime on $\mathbb{R}^{1,2} \times \mathbb{S}^1$.	contribution 0.81	0.88	0.04	asserted 0.89
s1	Static quarks are expected to be confined by double strings composed of two domain walls - which are lines in $\mathbb{R}^2$ - rather than by a single flux tube.	background 0.90	0.09	0.19	hedged possibility 0.97
s2	Each domain wall carries part of the quarks' chromoelectric flux.	background 0.95	0.12	0.04	asserted 1.00
s3	We numerically study this mechanism and find that double-string confinement holds for strings of all $N$-alities, except for those between fundamental quarks.	result 0.99	0.97	0.35	asserted 1.00
s4	We show that, for $N_c \ge 5$, the two domain walls confining unit $N$-ality quarks attract and form non-BPS bound states, collapsing to a single flux line.	result 1.00	0.94	0.34	asserted 1.00
s5	We determine the $N$-ality dependence of the string tensions for $2 \le N_c \le 10$.	contribution 0.75	0.96	0.06	asserted 0.99
s6	Compared to known scaling laws, we find a weaker, almost flat $N$-ality dependence, which is qualitatively explained by the properties of BPS domain walls.	result 0.85	0.97	0.14	asserted 1.00
s7	We also quantitatively study the behavior of confining strings upon increasing the $\mathbb{S}^1$ size by including the effect of virtual "$W$-bosons" and show that the qualitative features of double-string confinement persist.	result 0.57	0.96	0.10	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.98 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We study confining strings in ${\cal{N}}=1$ supersymmetric $SU(N_c)$ Yang-Mills theory in the semiclassical regime on $\mathbb{R}^{1,2} \times \mathbb{S}^1$. Static quarks are expected to be confined by double strings composed of two domain walls - which are lines in $\mathbb{R}^2$ - rather than by a single flux tube. Each domain wall carries part of the quarks' chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all $N$-alities, except for those between fundamental quarks. We show that, for $N_c \ge 5$, the two domain walls confining unit $N$-ality quarks attract and form non-BPS bound states, collapsing to a single flux line. We determine the $N$-ality dependence of the string tensions for $2 \le N_c \le 10$. Compared to known scaling laws, we find a weaker, almost flat $N$-ality dependence, which is qualitatively explained by the properties of BPS domain walls. We also quantitatively study the behavior of confining strings upon increasing the $\mathbb{S}^1$ size by including the effect of virtual "$W$-bosons" and show that the qualitative features of double-string confinement persist.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 2 Pith papers

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

Deconfinement on $\mathbb{Z}_{F}$ and Axion Domain Walls
hep-th 2026-10 accept novelty 7.0 of 10

In a center-stabilized compactification of QCD, probe particles of N-ality N/gcd(N,F) are deconfined on Z_F domain walls when gcd(N,F)>1, and the wall tensions differ from those in pure Yang-Mills.
Higher Representations and Quark Confinement
hep-th 2025-01 conditional novelty 6.0 of 10

Using higher-categorical representation theory, the paper proposes that the confined and adjoint Higgs phases of scalar QCD are distinguished by their baryon-charge spectra and by the presence of center vortices.

How the literature uses it

4 arXiv papers cite this in 11 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 · 10 sentences without a confident label

Cites it as background 1 paper

We can not discuss it any further and refer the reader to the literature (see [ref] , and, in a context related to our discussion, [ref] ; more references to the rather voluminous recent literature can be found there).[Let us mention also that there are phenomena related to the $θ=π$ domain walls and the deconfinement of probe quarks on their worldvolume whose unraveling demands going beyond the $μ≪1/L$ EFT, for example the braiding of fundamental Wilson loops on domain walls at $θ= π$ discussed in e.g. [ref] (this remark is also relevant for deconfinement on the QCD(adj) and SYM strings).

Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F) · $θ=π$: “double-string” confinement and deconfinement on domain walls. · 0.93

What it cites · 80 sentences without a confident label

Builds on 1 paper

The novelty of this paper is to make use of the analytical results of [ref] classifying the BPS DW fluxes (and the further insight into their properties) in $SU(N>2)$ SYM to study the double-string confinement mechanism for $SU(N)$ SYM.

Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow · Relation To (and Differences From) Confinement in the $^3$ Polyakov Model · 0.98

Uses the method or tool of 3 papers

The methods are mostly identical to those described in Sections 4 and 5 of [ref] , with some extensions and modifications.

Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow · Numerical Simulation of Double-String Configurations · 0.96
We further investigated the attraction and repulsion of DWs by numerically relaxing configurations consisting of the sum of two DWs similar to those depicted in Figure [ref] (this way of studying DW interactions is motivated by the “streamline" or “valley" method of [ref] , see also [ref] ).

Instantons in QCD · Attraction and Repulsion of Domain Walls · 0.99
Our computations for the confining string configurations were primarily performed on the Niagara cluster at the SciNet HPC Consortium [ref] .

Deploying a Top-100 Supercomputer for Large Parallel Workloads: the Niagara Supercomputer · Summary of Results and Outline · 0.95

Compares with 1 paper

This qualitatively matches with a simple model of exponential DW repulsion proposed earlier for an $SU(2)$ theory [ref] .

Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD · Summary of Results and Outline · 1.00

Cites as support 1 paper

This is, in fact, necessitated by the new mixed discrete chiral/center symmetry anomaly, as discussed already in [ref] .

Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow · Relation To (and Differences From) Confinement in the $^3$ Polyakov Model · 0.98

Cites as background 20 papers

But first, we remind the reader of the results of [ref] , which are essential for our arguments.

Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow · BPS DW Fluxes and Double-String Configurations · 0.81
Of special interest to us in this paper is the theory formulated on $^3 ×^1$, with supersymmetric boundary conditions on $^1$ [ref] .

Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions · Introduction, Summary, and Outlook · 0.95
Of special interest to us in this paper is the theory formulated on $^3 ×^1$, with supersymmetric boundary conditions on $^1$ [ref] .

Gauge Dynamics And Compactification To Three Dimensions · Introduction, Summary, and Outlook · 0.95

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.