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On AGT Conjecture for Pure Super Yang-Mills and W-algebra
High Energy Physics - Theory · Submitted 24 Dec 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We propose a simple relation between the Shapovalov matrix of the W_3-algebra and the Nekrasov partition function of N=2 SU(3) Yang-Mills theory.
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The abstract, sentence by sentence
Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal blocks associated with the conformal algebra. Likewise, a counterpart in pure super Yang-Mills theory exists in conformal field theory. We propose a simple relation between the Shapovalov matrix of the W_3-algebra and the Nekrasov partition function of N=2 SU(3) Yang-Mills theory.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. | background 1.00 | 0.03 | 0.03 | asserted 1.00 |
| s1 | The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal blocks associated with the conformal algebra. | background 0.99 | 0.06 | 0.07 | asserted 0.99 |
| s2 | Likewise, a counterpart in pure super Yang-Mills theory exists in conformal field theory. | background 0.96 | 0.10 | 0.06 | asserted 0.98 |
| s3 | We propose a simple relation between the Shapovalov matrix of the W_3-algebra and the Nekrasov partition function of N=2 SU(3) Yang-Mills theory. | contribution 0.88 | 0.92 | 0.89 | asserted 0.68 |
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The paper
Original abstract
Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal blocks associated with the conformal algebra. Likewise, a counterpart in pure super Yang-Mills theory exists in conformal field theory. We propose a simple relation between the Shapovalov matrix of the W_3-algebra and the Nekrasov partition function of N=2 SU(3) Yang-Mills theory.
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References
How the literature uses it
40 arXiv papers cite this in 60 sentences
Papers citing it · 40 sentences without a confident label
Builds on it 2 papers
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This conjecture is precisely 5d generalization of the AGT-W correspondence between 4d $SU(3)$ pure Yang-Mills theory and the $W_3$ algebra proposed in [ref] .
On AGT-W Conjecture and q-Deformed W-Algebra · $SU(3)$ Yang-Mills versus $q$-$W_3$ algebra · 0.94
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The aim of this paper is to rectify the situation, by studying $=2$ pure gauge theory for arbitrary $G$ as an extension of [ref] .
The ABCDEFG of Instantons and W-algebras · Introduction · 1.00
Uses its method or tool 1 paper
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The method is the same as in [ref] .
The ABCDEFG of Instantons and W-algebras · Coherent state at the lowest level · 1.00
Uses its data or values 1 paper
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The Gram/Shapovalov matrix is K(Y_1,Y_2;Y_1,Y_2)=W_Y_2L_Y_1·L_-Y_1W_-Y_2.The first two level CFT data are given in [ref] , we also give them in the Appendix[ref].
A note on W symmetry of N=2 gauge theory · Irregular conformal block for A$_2$ Toda CFT · 0.86
Compares with it 2 papers
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The corresponding bra is given by [equation] Now, it can be checked that [equation] Therefore, [equation] which is indeed the one-instanton contribution of Nekrasov's partition function [ref] calculated from the geometry of the one-instanton moduli space.
The ABCDEFG of Instantons and W-algebras · $A_n$ · 0.86
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Our conjecture simplifies the original 4d AGT-W correspondence [ref] since we can write down the algebraic relations of the $q$-deformed $W_N$ algebra explicitly, although it is very hard to find the explicit form for the undeformed one.
On AGT-W Conjecture and q-Deformed W-Algebra · Discussion · 0.86
Cites it as support 1 paper
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For various case, it has been shown in [ref] by some explicit calculations that the Gaiotto state of Toda CFT indeed gives gauge theory instanton partition.
A note on W symmetry of N=2 gauge theory · Irregular conformal block and Gaiotto state · 0.99
Cites it as background 13 papers
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The AGT correspondence [ref] relates $= 2$ supersymmetric gauge theories in four dimensions and conformal field theories with W-algebra symmetry in two dimensions [ref] .
Compactification on the \Omega-background and the AGT correspondence · Introduction · 0.99
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One highlight is a conjectural relation between these theories and conformal field theories (CFT) in two dimensions, formulated by Alday, Gaiotto and Tachikawa [ref] (AGT) and generalized thereafter by others [ref] .
On the six-dimensional origin of the AGT correspondence · Introduction · 0.97
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This correspondence has been generalized for the conformal theories with additional symmetries, such as affine Lie algebras, $W$ algebras, parafermions [ref] .
Instantons and 2d Superconformal field theory · Introduction · 0.84
What it cites · 39 sentences without a confident label
Builds on 2 papers
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Our proposal is a simple and nontrivial extension of the Gaiotto-Marshakov-Mironov proposal [ref] [ref] , and it suggests that there exists a direct connection between instanton counting and conformal symmetry.
Asymptotically free N=2 theories and irregular conformal blocks · Conclusion · 0.99
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Our proposal is a simple and nontrivial extension of the Gaiotto-Marshakov-Mironov proposal [ref] [ref] , and it suggests that there exists a direct connection between instanton counting and conformal symmetry.
On non-conformal limit of the AGT relations · Conclusion · 0.99
Uses the method or tool of 2 papers
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The key is the Mironov-Mironov-Morozov-Morozov recursion relations [ref] for a descendant $V_a$: [equation]
CFT exercises for the needs of AGT · recursion relations and asymptotic behavior · 0.99
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Let us introduce the following parametrization [ref] of the gauge theory parameters: [equation] Here $e$ denotes $e=e_1+e_2$.
Liouville Correlation Functions from Four-dimensional Gauge Theories · Alday-Gaiotto-Tachikawa conjecture · 0.83
Uses data or values from 2 papers
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The level-$1$ Shapovalov matrix is [ref] [ref] [equation] where the label is $𝒴=(Y_L,Y_W)$.
CFT exercises for the needs of AGT · Check · 0.80
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The level-$1$ Shapovalov matrix is [ref] [ref] [equation] where the label is $𝒴=(Y_L,Y_W)$.
On AGT relation in the case of U(3) · Check · 0.80
Cites as background 12 papers
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AGT-W conjecture [ref] gives relation between $SU(N_c)$ $N_f=2N_c$ gauge theory and the conformal Toda theory with $𝒲_N$-symmetry.
A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories · AGT-W relation for $N_c=3$, $N_f=6$ gauge theory · 0.94
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Recently, remarkable relation between 2- and 4-dimensonal CFT's was proposed by Alday, Gaiotto and Tachikawa [ref] .
Liouville Correlation Functions from Four-dimensional Gauge Theories · Introduction · 0.92
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The Nekrasov partition function [ref] is a generating function of the Seiberg-Witten prepotential $Z^inst=exp(1/ϵ_1ϵ_2 ℱ^SW+⋯)$.
Seiberg-Witten Prepotential From Instanton Counting · Alday-Gaiotto-Tachikawa conjecture · 0.96
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