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Computing the \theta-exact Seiberg-Witten map for arbitrary gauge groups
High Energy Physics - Theory · Submitted 13 Jun 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For gauge and matter fields, we fully work out \theta-exact non-hybrid Seiberg-Witten maps up to order three in the number of ordinary gauge fields.
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We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in the gauge coupling constant or, equivalently, in the number of ordinary gauge fields. We do so for arbitrary compact gauge groups in arbitrary unitary representations. For gauge and matter fields, we fully work out \theta-exact non-hybrid Seiberg-Witten maps up to order three in the number of ordinary gauge fields.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in the gauge coupling constant or, equivalently, in the number of ordinary gauge fields. | method 0.92 | 0.61 | 0.23 | asserted 0.91 |
| s1 | We do so for arbitrary compact gauge groups in arbitrary unitary representations. | contribution 0.95 | 0.85 | 0.11 | asserted 0.99 |
| s2 | For gauge and matter fields, we fully work out \theta-exact non-hybrid Seiberg-Witten maps up to order three in the number of ordinary gauge fields. | contribution 0.64 | 0.95 | 0.51 | asserted 1.00 |
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The paper
Original abstract
We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in the gauge coupling constant or, equivalently, in the number of ordinary gauge fields. We do so for arbitrary compact gauge groups in arbitrary unitary representations. For gauge and matter fields, we fully work out \theta-exact non-hybrid Seiberg-Witten maps up to order three in the number of ordinary gauge fields.
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How the literature uses it
11 arXiv papers cite this in 35 sentences
Papers citing it · 23 sentences without a confident label
Builds on it 1 paper
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Following the recent results on higher order $θ$-exact Seiberg-Witten map [ref] , we present here the full $θ$-exact four photon self-interaction in the SW mapped deformed pure U(1) gauge theory on Moyal space and the evaluation of the resulting four-photon tadpole diagram, thus complete the one loop corrections to the photon polarization tensor.
Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution · Introduction · 0.81
Uses its method or tool 7 papers
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[ref] by appropriate symmetrization.
Quantum duality under the theta-exact Seiberg-Witten map · No one-loop two-point contribution coming from $J_1[B,Q]$ nor $J_2[B,Q]$. · 0.81
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To cure the cut-off approximation, we are using $θ$-exact expressions, inspired by exact formulas for the SW map [ref] , and expand in powers of gauge fields, as we did in [ref] .
Noncommutative geometry in quantum field theory and the cosmogenic neutrino physics at the extreme energies · Introduction · 0.95
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To cure the cut-off approximation, we are using $θ$-exact expressions, inspired by exact formulas for the SW map [ref] , and expand in powers of gauge fields, as we did in [ref] .
High energy cosmic rays experiments inspired by noncommutative quantum field theory · Introduction · 0.96
What it cites · 7 sentences without a confident label
Builds on 2 papers
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Then, the results presented in ([ref]) also hold for $G$, if $g a_μ$ is replaced with the whole ordinary gauge field, $v_μ$, defined [ref] as follows [equation] ${(T^(k))^a, T^(l)}$, with $a=1,...,dim G_k$ for every $k=1,...,s$, stand for the generators of the gauge group $G$ in a given unitary irreducible representation.
Anomaly freedom in Seiberg-Witten noncommutative gauge theories · The $θ$-exact Seiberg-Witten map equations and their solution · 0.97
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Then, the analysis of the UV/IR mixing was extended [ref] to fermions in the fundamental coupled to $U(1)$ gauge fields.
On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED · Introduction · 0.82
Cites as background 21 papers
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A dozen years ago, it was put forward a formalism –the enveloping-algebra formalism– which can be used to construct noncommutative gauge theories that are deformations of ordinary theories with simple gauge groups in arbitrary unitary representations [ref] .
Construction of non-Abelian gauge theories on noncommutative spaces · Introduction · 0.94
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A dozen years ago, it was put forward a formalism –the enveloping-algebra formalism– which can be used to construct noncommutative gauge theories that are deformations of ordinary theories with simple gauge groups in arbitrary unitary representations [ref] .
Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces · Introduction · 0.94
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A dozen years ago, it was put forward a formalism –the enveloping-algebra formalism– which can be used to construct noncommutative gauge theories that are deformations of ordinary theories with simple gauge groups in arbitrary unitary representations [ref] .
Gauge Theory on Noncommutative Spaces · Introduction · 0.94
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