{"arxiv_id":"1303.4237","incoming":{"papers":6,"sentences":7,"groups":[{"kind":"background","label":"Cites it as background","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1309.1687","title":"Gauge/Liouville Triality","url":"/paper/1309.1687","section":"M-theory and Large $N$ transitions","sentence":"The relation was revisited in [ref] , who studied the theories in the NS limit [ref] , and interpreted the duality in the context of integrable systems (see also [ref] ).","intent_p":0.94,"contests_p":null},{"arxiv_id":"1307.1502","title":"Spectral dualities in XXZ spin chains and five dimensional gauge theories","url":"/paper/1307.1502","section":"Introduction","sentence":"Different aspects and applications of the spectral duality can be found in [ref] .","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":5},"outgoing":{"papers":32,"sentences":92,"groups":[{"kind":"extends","label":"Builds on","papers":4,"sentences":7,"quotes":[{"arxiv_id":"1103.5726","title":"Quantization of Integrable Systems and a 2d/4d Duality","url":"/paper/1103.5726","section":"Introduction","sentence":"We generalize the exact field theoretic correspondence proposed in [ref] and embed it into the context of refined topological string.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1104.3021","title":"A New 2d/4d Duality via Integrability","url":"/paper/1104.3021","section":"Nekrasov-Shatashivili limit and Saddle Point Approximation","sentence":"Here we begin by discussing the simple K-theoretic generalization of the exact correspondence proposed in [ref] , and in the later sections we shall consider the realization of these gauge theories in the M-theory interpretation of the refined topological string, and how the exact correspondence discovered in [ref] can be recast as a beautiful realization of refined geometric transition.","intent_p":0.97,"contests_p":null},{"arxiv_id":"1006.0977","title":"Vortex Counting and Lagrangian 3-manifolds","url":"/paper/1006.0977","section":"Single Stack of Surface Operators : $n⃗=(0,0, …n_s, …0, 0)$","sentence":"Here as a consistency check, we consider the single stack of toric brane insertion with only $n_s ≠0$ for the Abelian factor $U(1)_s$, they are labeled by a Young diagram with $n_s$ columns, this should be regarded as a slight generalization of the refined geometric transition involving single toric brane considered in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1007.2524","title":"Surface Operator, Bubbling Calabi-Yau and AGT Relation","url":"/paper/1007.2524","section":"Single Stack of Surface Operators : $n⃗=(0,0, …n_s, …0, 0)$","sentence":"Here as a consistency check, we consider the single stack of toric brane insertion with only $n_s ≠0$ for the Abelian factor $U(1)_s$, they are labeled by a Young diagram with $n_s$ columns, this should be regarded as a slight generalization of the refined geometric transition involving single toric brane considered in [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":4,"sentences":7,"quotes":[{"arxiv_id":"0805.0191","title":"Refined BPS state counting from Nekrasov's formula and Macdonald functions","url":"/paper/0805.0191","section":"Truncated Partition Function and Surface Operators","sentence":"Here we can use another representation of the function $_Y_l Y_k(Q; q, t)$ and its symmetry property as proven in [ref] , [equation] to rewrite ([ref]) into a suitable form for comparison with the open refined topological string computation.","intent_p":0.9,"contests_p":null},{"arxiv_id":"0710.1776","title":"Refined Topological Vertex and Instanton Counting","url":"/paper/0710.1776","section":"The Closed Refined Topological String","sentence":"The closed refined topological string can then be recast into the five dimensional gauge theory instanton partition function with $N_f=2N_c$, using the formulae provided in [ref] , see also [ref] for higher rank generalization.","intent_p":0.91,"contests_p":null},{"arxiv_id":"1007.2524","title":"Surface Operator, Bubbling Calabi-Yau and AGT Relation","url":"/paper/1007.2524","section":"Open string partition function","sentence":"Following the derivation outlined in [ref] one can also easily find the effective superpotential and the associated Gaiotto curve from the open string partition function.","intent_p":0.95,"contests_p":null},{"arxiv_id":"1004.5122","title":"Five-dimensional AGT Relation and the Deformed beta-ensemble","url":"/paper/1004.5122","section":"Nekrasov-Shatashivili limit and Saddle Point Approximation","sentence":"Here we begin by expressing it in terms of products of Pochhammer symbol [ref] : [equation] where $Y⃗=(Y_1,Y_2,…, Y_N_c)$ is a set of Young diagrams whose columns satisfy $Y_l1≥Y_l2≥…$, for the time being the number of the columns in each Young diagram can be arbitrary.","intent_p":0.96,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":2,"sentences":6,"quotes":[{"arxiv_id":"0710.1776","title":"Refined Topological Vertex and Instanton Counting","url":"/paper/0710.1776","section":"The Closed Refined Topological String","sentence":"This agrees completely with (3.2) of [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1007.2524","title":"Surface Operator, Bubbling Calabi-Yau and AGT Relation","url":"/paper/1007.2524","section":"Appendix B: Superpotenial from the open string partition function","sentence":"This also means that in the NS limit we obtain the same Gaiotto curve of 4d supersymmetric gauge theory, with a shift in its parameters[ In the limit $ϵ_2 →0$ or superpotential becomes precisely that of (2.14) [ref] .].","intent_p":0.9,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1103.5726","title":"Quantization of Integrable Systems and a 2d/4d Duality","url":"/paper/1103.5726","section":"Introduction","sentence":"As an initial step, in [ref] a new exact correspondence between the quantum vacua of four dimensional $=2$ supersymmetric gauge theories and two dimensional $=(2,2)$ gauged linear sigma models was proposed, as both sets of vacua can be identified with the eigenstates of the same quantum integrable Hamiltonian under specific conditions for the parameters.","intent_p":0.82,"contests_p":null},{"arxiv_id":"1104.3021","title":"A New 2d/4d Duality via Integrability","url":"/paper/1104.3021","section":"Introduction","sentence":"As an initial step, in [ref] a new exact correspondence between the quantum vacua of four dimensional $=2$ supersymmetric gauge theories and two dimensional $=(2,2)$ gauged linear sigma models was proposed, as both sets of vacua can be identified with the eigenstates of the same quantum integrable Hamiltonian under specific conditions for the parameters.","intent_p":0.82,"contests_p":null}]}],"unlabelled_sentences":70},"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/1303.4237"}}