{"arxiv_id":"0912.4789","incoming":{"papers":40,"sentences":60,"groups":[{"kind":"extends","label":"Builds on it","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1403.7016","title":"On AGT-W Conjecture and q-Deformed W-Algebra","url":"/paper/1403.7016","section":"$SU(3)$ Yang-Mills versus $q$-$W_3$ algebra","sentence":"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] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"1111.5624","title":"The ABCDEFG of Instantons and W-algebras","url":"/paper/1111.5624","section":"Introduction","sentence":"The aim of this paper is to rectify the situation, by studying $=2$ pure gauge theory for arbitrary $G$ as an extension of [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1111.5624","title":"The ABCDEFG of Instantons and W-algebras","url":"/paper/1111.5624","section":"Coherent state at the lowest level","sentence":"The method is the same as in [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1206.2844","title":"A note on W symmetry of N=2 gauge theory","url":"/paper/1206.2844","section":"Irregular conformal block for A$_2$ Toda CFT","sentence":"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].","intent_p":0.86,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1111.5624","title":"The ABCDEFG of Instantons and W-algebras","url":"/paper/1111.5624","section":"$A_n$","sentence":"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.","intent_p":0.86,"contests_p":null},{"arxiv_id":"1403.7016","title":"On AGT-W Conjecture and q-Deformed W-Algebra","url":"/paper/1403.7016","section":"Discussion","sentence":"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.","intent_p":0.86,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1206.2844","title":"A note on W symmetry of N=2 gauge theory","url":"/paper/1206.2844","section":"Irregular conformal block and Gaiotto state","sentence":"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.","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":13,"sentences":13,"quotes":[{"arxiv_id":"1205.6820","title":"Compactification on the \\Omega-background and the AGT correspondence","url":"/paper/1205.6820","section":"Introduction","sentence":"The AGT correspondence [ref] relates $= 2$ supersymmetric gauge theories in four dimensions and conformal field theories with W-algebra symmetry in two dimensions [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1112.0260","title":"On the six-dimensional origin of the AGT correspondence","url":"/paper/1112.0260","section":"Introduction","sentence":"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] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"1106.4001","title":"Instantons and 2d Superconformal field theory","url":"/paper/1106.4001","section":"Introduction","sentence":"This correspondence has been generalized for the conformal theories with additional symmetries, such as affine Lie algebras, $W$ algebras, parafermions [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"1004.1841","title":"Proving the AGT relation for N_f = 0,1,2 antifundamentals","url":"/paper/1004.1841","section":"Introduction","sentence":"Other extensions concern non-conformal limit of the AGT [ref] correspondence and its 5-dimensional version [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"1109.0004","title":"Beta-ensembles for toric orbifold partition function","url":"/paper/1109.0004","section":"Introduction","sentence":"The remarkable connection between the four and two dimensional theories through the instanton partition function is called AGT relation [ref] , and generalized to various situations, for example, the higher rank theory [ref] , the asymptotic free theory [ref] and also the ALE space [ref] , etc.","intent_p":0.87,"contests_p":null}]}],"unlabelled_sentences":40},"outgoing":{"papers":23,"sentences":57,"groups":[{"kind":"extends","label":"Builds on","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0908.0307","title":"Asymptotically free N=2 theories and irregular conformal blocks","url":"/paper/0908.0307","section":"Conclusion","sentence":"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.","intent_p":0.99,"contests_p":null},{"arxiv_id":"0909.2052","title":"On non-conformal limit of the AGT relations","url":"/paper/0909.2052","section":"Conclusion","sentence":"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.","intent_p":0.99,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0908.2064","title":"CFT exercises for the needs of AGT","url":"/paper/0908.2064","section":"recursion relations and asymptotic behavior","sentence":"The key is the Mironov-Mironov-Morozov-Morozov recursion relations [ref] for a descendant $V_a$: [equation]","intent_p":0.99,"contests_p":null},{"arxiv_id":"0906.3219","title":"Liouville Correlation Functions from Four-dimensional Gauge Theories","url":"/paper/0906.3219","section":"Alday-Gaiotto-Tachikawa conjecture","sentence":"Let us introduce the following parametrization [ref] of the gauge theory parameters: [equation] Here $e$ denotes $e=e_1+e_2$.","intent_p":0.83,"contests_p":null}]},{"kind":"data_used","label":"Uses data or values from","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0908.2064","title":"CFT exercises for the needs of AGT","url":"/paper/0908.2064","section":"Check","sentence":"The level-$1$ Shapovalov matrix is [ref] [ref] [equation] where the label is $𝒴=(Y_L,Y_W)$.","intent_p":0.8,"contests_p":null},{"arxiv_id":"0908.2569","title":"On AGT relation in the case of U(3)","url":"/paper/0908.2569","section":"Check","sentence":"The level-$1$ Shapovalov matrix is [ref] [ref] [equation] where the label is $𝒴=(Y_L,Y_W)$.","intent_p":0.8,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":12,"sentences":12,"quotes":[{"arxiv_id":"0907.2189","title":"A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories","url":"/paper/0907.2189","section":"AGT-W relation for $N_c=3$, $N_f=6$ gauge theory","sentence":"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.","intent_p":0.94,"contests_p":null},{"arxiv_id":"0906.3219","title":"Liouville Correlation Functions from Four-dimensional Gauge Theories","url":"/paper/0906.3219","section":"Introduction","sentence":"Recently, remarkable relation between 2- and 4-dimensonal CFT's was proposed by Alday, Gaiotto and Tachikawa [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"hep-th/0206161","title":"Seiberg-Witten Prepotential From Instanton Counting","url":"/paper/hep-th/0206161","section":"Alday-Gaiotto-Tachikawa conjecture","sentence":"The Nekrasov partition function [ref] is a generating function of the Seiberg-Witten prepotential $Z^inst=exp(1/ϵ_1ϵ_2 ℱ^SW+⋯)$.","intent_p":0.96,"contests_p":null},{"arxiv_id":"0908.0307","title":"Asymptotically free N=2 theories and irregular conformal blocks","url":"/paper/0908.0307","section":"Gaiotto conjecture (non-conformal AGT conjecture)","sentence":"In [ref] Gaiotto proposed that the partition function is realized as the norm of a certain state of the Virasoro algebra: [equation] Here we eliminate the overall scale scale $ħ$ from the parameters, and the conformal dimension of the internal state is $Δ=a^2-e^2/4$.","intent_p":0.83,"contests_p":null},{"arxiv_id":"0908.2569","title":"On AGT relation in the case of U(3)","url":"/paper/0908.2569","section":"structure of correlators","sentence":"See [ref] [ref] [ref] for details.","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":39},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/0912.4789"}}