Comments on Instantons on Noncommutative R^4

Bum-Hoon Lee; Hyun Seok Yang; Keun-Young Kim

RECORD

Comments on Instantons on Noncommutative R^4

Keun-Young Kim, Bum-Hoon Lee, Hyun Seok Yang

High Energy Physics - Theory · Submitted 13 Mar 2000

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

The authors' main claim It is shown that the anti-self-dual gauge fields on self-dual noncommutative R^4 correctly give integer instanton numbers for all cases we consider.

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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,959 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.28 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We study U(1) and U(2) instanton solutions on noncommutative R^4 based on the noncommutative version of ADHM equation proposed by Nekrasov and Schwarz. It is shown that the anti-self-dual gauge fields on self-dual noncommutative R^4 correctly give integer instanton numbers for all cases we consider. We also show that the completeness relation in the ADHM construction is generally satisfied even for noncommutative spaces.

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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 U(1) and U(2) instanton solutions on noncommutative R^4 based on the noncommutative version of ADHM equation proposed by Nekrasov and Schwarz.	contribution 0.98	0.87	0.07	asserted 0.83
s1	It is shown that the anti-self-dual gauge fields on self-dual noncommutative R^4 correctly give integer instanton numbers for all cases we consider.	result 1.00	0.90	0.49	asserted 1.00
s2	We also show that the completeness relation in the ADHM construction is generally satisfied even for noncommutative spaces.	result 0.99	0.93	0.19	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.88 · evidence from proof or derivation 1.00.

What was examined, and what was not

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arXiv listing abstract v4

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full text
figures and tables
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P abstract

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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 U(1) and U(2) instanton solutions on noncommutative R^4 based on the noncommutative version of ADHM equation proposed by Nekrasov and Schwarz. It is shown that the anti-self-dual gauge fields on self-dual noncommutative R^4 correctly give integer instanton numbers for all cases we consider. We also show that the completeness relation in the ADHM construction is generally satisfied even for noncommutative spaces.

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References

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2 arXiv papers cite this in 6 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 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 prove the results announced in a joint paper (arXiv:hep-th/0603106) with Maxim Kontsevich and Albert Schwarz.

Integrality of instanton numbers · 0.80

Papers citing it · 3 sentences without a confident label

Cites it as background 2 papers

Let us first discuss the usual single anti-self-dual $U(1)$ instanton solutions ($k=1, N=1$) in $ℝ^2_NC×ℝ^2_C$ [ref] and in $ℝ^2_NC×ℝ^2_NC$ [ref] .

Noncommutative Vortices and Instantons from Generalized Bose Operators · Noncommutative ADHM Construction · 0.91
Let us first discuss the usual single anti-self-dual $U(1)$ instanton solutions ($k=1, N=1$) in $R^2_NC×R^2_C$ [ref] and in $R^2_NC×R^2_NC$ [ref] .

Topics in Noncommutative Gauge Theories and Deformed Relativistic Theories · Noncommutative ADHM Construction · 0.89

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