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Solitons in Noncommutative Gauge Theory

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David J. Gross, Nikita A. Nekrasov

High Energy Physics - Theory · Submitted 11 Oct 2000

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

The authors' main claim We present a unified treatment of classical solutions of noncommutative gauge theories.

how it is stated · asserted 0.98 read the record →

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arXiv IDhep-th/0010090 (version 1)
Pith IDNR6MBYO2, Pith's permanent record of this paper and its review
CitationDavid J. Gross, Nikita A. Nekrasov. "Solitons in Noncommutative Gauge Theory." arXiv:hep-th/0010090 (2000). https://pith.science/paper/NR6MBYO2
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,607 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.43 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We present a unified treatment of classical solutions of noncommutative gauge theories. We find all solutions of the noncommutative Yang-Mills equations in 2 dimensions; and show that they are labelled by two integers -- the rank of gauge group and the magnetic charge. The magnetic vortex solutions are unstable in 2+1 dimensions, but correspond to the full, stable BPS solutions of N=4 U(1) noncommutative gauge theory in 4 dimensions, that describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B field in the Seiberg-Witten limit. We discuss the behaviour of gauge invariant observables in the background of the solitons. We use these solutions to construct a panoply of BPS and non-BPS solutions of supersymmetric gauge theories that describe various configurations of D-branes. We analyze the instabilities of the non-BPS solutions. We also present an exact analytic solution of noncommutative gauge theory that describes a U(2) monopole.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a unified treatment of classical solutions of noncommutative gauge theories. contribution 1.00 0.94 0.13 asserted 0.98
s1 We find all solutions of the noncommutative Yang-Mills equations in 2 dimensions; and show that they are labelled by two integers -- the rank of gauge group and the magnetic charge. result 0.93 0.96 0.31 asserted 1.00
s2 The magnetic vortex solutions are unstable in 2+1 dimensions, but correspond to the full, stable BPS solutions of N=4 U(1) noncommutative gauge theory in 4 dimensions, that describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B field in the Seiberg-Witten limit. result 0.76 0.72 0.26 asserted 1.00
s3 We discuss the behaviour of gauge invariant observables in the background of the solitons. contribution 0.99 0.86 0.05 asserted 0.52
s4 We use these solutions to construct a panoply of BPS and non-BPS solutions of supersymmetric gauge theories that describe various configurations of D-branes. contribution 0.90 0.94 0.17 asserted 1.00
s5 We analyze the instabilities of the non-BPS solutions. contribution 0.97 0.93 0.05 asserted 0.75
s6 We also present an exact analytic solution of noncommutative gauge theory that describes a U(2) monopole. result 0.64 0.95 0.11 asserted 1.00

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

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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 present a unified treatment of classical solutions of noncommutative gauge theories. We find all solutions of the noncommutative Yang-Mills equations in 2 dimensions; and show that they are labelled by two integers -- the rank of gauge group and the magnetic charge. The magnetic vortex solutions are unstable in 2+1 dimensions, but correspond to the full, stable BPS solutions of N=4 U(1) noncommutative gauge theory in 4 dimensions, that describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B field in the Seiberg-Witten limit. We discuss the behaviour of gauge invariant observables in the background of the solitons. We use these solutions to construct a panoply of BPS and non-BPS solutions of supersymmetric gauge theories that describe various configurations of D-branes. We analyze the instabilities of the non-BPS solutions. We also present an exact analytic solution of noncommutative gauge theory that describes a U(2) monopole.

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References
How the literature uses it

10 arXiv papers cite this in 16 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 · 9 sentences without a confident label

Uses its method or tool 3 papers
  • According to the Nahm construction of monopoles in non-commutative space [ref] , this equation is exactly the one to solve for the construction of all solutions satisfying the BPS monopole equation in the non-commutative space, [equation] where the scalar field $Φ$ and the gauge field $A_i$ are functions of the non-commutative coordinates $(p̂_1,p̂_2,p_3)$.

    Topological Number of Edge States · Magnetic field, non-commutative space and D-brane · 0.96

  • More general solutions can be found using the solution generating technique which applies partial gauge transformations to the vacuum solution [ref] [ref] .

    Noncommutative Instantons in Diverse Dimensions · Explicit Solutions · 0.96

  • A large class of nontrivial solutions can be produced using the solution generating technique [ref] .

    Tetrahedron instantons · Noncommutative instantons · 0.93

Cites it as background 4 papers

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