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Compactification on the \Omega-background and the AGT correspondence
High Energy Physics - Theory · Submitted 30 May 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that the expectation values of its currents determine the Seiberg-Witten curve of the four-dimensional side.
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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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The abstract, sentence by sentence
The six-dimensional (2,0) theory formulated in the \Omega-background gives rise to two-dimensional effective degrees of freedom. By compactifying the theory on the circle fibers of two cigar-like manifolds, we find that a natural candidate for the effective theory is a chiral gauged WZW model. The symmetry algebra of the model contains the W-algebra that appears on the two-dimensional side of the AGT correspondence. We show that the expectation values of its currents determine the Seiberg-Witten curve of the four-dimensional side.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The six-dimensional (2,0) theory formulated in the \Omega-background gives rise to two-dimensional effective degrees of freedom. | background 0.74 | 0.21 | 0.09 | asserted 1.00 |
| s1 | By compactifying the theory on the circle fibers of two cigar-like manifolds, we find that a natural candidate for the effective theory is a chiral gauged WZW model. | method 0.42 | 0.93 | 0.23 | asserted 0.70 |
| s2 | The symmetry algebra of the model contains the W-algebra that appears on the two-dimensional side of the AGT correspondence. | result 0.95 | 0.47 | 0.22 | asserted 1.00 |
| s3 | We show that the expectation values of its currents determine the Seiberg-Witten curve of the four-dimensional side. | result 0.97 | 0.91 | 0.52 | asserted 1.00 |
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The paper
Original abstract
The six-dimensional (2,0) theory formulated in the \Omega-background gives rise to two-dimensional effective degrees of freedom. By compactifying the theory on the circle fibers of two cigar-like manifolds, we find that a natural candidate for the effective theory is a chiral gauged WZW model. The symmetry algebra of the model contains the W-algebra that appears on the two-dimensional side of the AGT correspondence. We show that the expectation values of its currents determine the Seiberg-Witten curve of the four-dimensional side.
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References
How the literature uses it
14 arXiv papers cite this in 19 sentences
Papers citing it · 9 sentences without a confident label
Compares with it 1 paper
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This perspective on AGT is similar to the point of view of [ref] .
Toda Theory From Six Dimensions · Overview of the Derivation · 0.95
Cites it as background 8 papers
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Recently, a derivation of the AGT correspondence via reduction of 6d CFT to $M^4$ and $Σ^2$ was discussed in [ref] .
Dual infrared limits of 6d $\cal N$=(2,0) theory · Introduction and summary · 0.88
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The classical example of this procedure are 6d $(2,0)$ SCFTs on an $×_ϵ_1×_ϵ_2$ background [ref] .
Aspects of $\Omega$-deformed M-theory · $Ω$-deformation and compactification: the M5 brane case · 0.90
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It is well-known that the $_N$-algebra is the vertex algebra of local operators in a six-dimensional $=(2,0)$ superconformal theory, subject to the $Ø$-background [ref] .
R-matrices and Miura operators in 5d Chern-Simons theory · Introduction · 0.89
What it cites · 30 sentences without a confident label
Compares with 1 paper
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For example, for $= A_N-1$ we have [equation] and we find the correspondence [equation] Essentially the same relation was proposed in [ref] .
Hitchin systems, N=2 gauge theories and W-gravity · The AGT correspondence · 0.90
Cites as support 3 papers
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This relation was conjectured in [ref] , and has been checked in [ref] .
Liouville Correlation Functions from Four-dimensional Gauge Theories · The AGT correspondence · 0.97
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This relation was conjectured in [ref] , and has been checked in [ref] .
N=2 gauge theories and degenerate fields of Toda theory · The AGT correspondence · 0.97
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This relation was conjectured in [ref] , and has been checked in [ref] .
The ABCDEFG of Instantons and W-algebras · The AGT correspondence · 0.97
Cites as background 8 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] .
Liouville Correlation Functions from Four-dimensional Gauge Theories · Introduction · 0.99
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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] .
A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories · Introduction · 0.99
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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] .
On AGT relation in the case of U(3) · Introduction · 0.99
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