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Dipoles, Twists and Noncommutative Gauge Theory
High Energy Physics - Theory · Submitted 2 Aug 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions.
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The abstract, sentence by sentence
T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude. Several unique properties of field theories on noncommutative spaces have simpler counterparts in the dipole-theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. | contribution 0.78 | 0.50 | 0.24 | asserted 0.83 |
| s1 | The resulting T-dual theories contain novel nonlocal fields. | result 0.97 | 0.73 | 0.21 | asserted 1.00 |
| s2 | These fields represent dipoles of constant magnitude. | interpretation 0.50 | 0.58 | 0.21 | asserted 1.00 |
| s3 | Several unique properties of field theories on noncommutative spaces have simpler counterparts in the dipole-theories. | interpretation 0.81 | 0.48 | 0.24 | asserted 0.99 |
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The paper
Original abstract
T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude. Several unique properties of field theories on noncommutative spaces have simpler counterparts in the dipole-theories.
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References
How the literature uses it
42 arXiv papers cite this in 70 sentences
Papers citing it · 42 sentences without a confident label
Uses its method or tool 1 paper
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To overcome this, we recall that for dipole-theories there is a way to rewrite [ref] so that only the field strength $F_μν=2∂_[μA_ν]$ appears [ref] .
Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings · Cubic terms · 0.89
Compares with it 1 paper
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Denoting the dressed S-matrix as $S_μ^a$, the incoming charges and momenta as $q^i,p_a^i$ and the outgoing charges and momenta as $q̅^j, p̅_a^j$, the final result for the dressed S-matrix is S_μ^a({p^i,q^i}→{p̅^j,q̅^j})=e^-iμ^a ∑_i<j(q^i p^j_a-q^j p^i_a)e^-iμ^a ∑_i<j(q̅^i p̅^j_a-q̅^j p̅^i_a)S_0 ({p^i,q^i}→{p̅^j,q̅^j}) Notice that the above dressing is identical to that found in planar diagrams of noncommutative dipole field theories [ref] with $μ^a$ identified with the dipole length.
A general definition of $JT_a$ -- deformed QFTs · Derivation of the dressing factor · 0.99
Cites it as support 1 paper
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As was suggested in [ref] , such theories arise naturally in M-theory.
Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings · Introduction · 0.97
Cites it as background 21 papers
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The holographic dual of the $Sch_5 ×S^5$ background is obtained by applying a TsT transformation to the theory living on a stack of D3 branes and taking the decoupling limit [ref] .
Integrability in dipole-deformed N=4 super Yang-Mills · The dipole deformation in field theory · 0.84
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In parallel with these developments, recent investigations have indicated an interesting class of nonlocal deformations of quantum field theory known as dipole deformations [ref] .
Warped AdS3/Dipole-CFT Duality · Introduction · 0.99
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Its deformations include: noncommutative Yang-Mills where the Neveu-Shwarz two form is present along the brane world volume [ref] ; the so called dipole theory where the Neveu-Schwarz two form is present with one leg along the brane world volume and one off it [ref] ; and finally the $𝒩=1$ $β$-deformed Yang-Mills theory where the Neveu Schwarz two form is present entirely off the brane world volume [ref] .
M-Theory Brane Deformations · Introduction · 0.92
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