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On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
High Energy Physics - Theory · Submitted 18 Mar 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The correspondence originally proposed from the common integrable structures in different field theories can be recast as a special limit of the refined geometric transition relating open and closed topological string partition functions.
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The abstract, sentence by sentence
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field theories can be recast as a special limit of the refined geometric transition relating open and closed topological string partition functions. We realize the simplest examples of the correspondence explicitly in terms of open-closed geometric transition.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. | contribution 1.00 | 0.91 | 0.16 | asserted 1.00 |
| s1 | The correspondence originally proposed from the common integrable structures in different field theories can be recast as a special limit of the refined geometric transition relating open and closed topological string partition functions. | contribution 0.44 | 0.38 | 0.55 | asserted 0.97 |
| s2 | We realize the simplest examples of the correspondence explicitly in terms of open-closed geometric transition. | contribution 0.80 | 0.92 | 0.23 | asserted 1.00 |
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The paper
Original abstract
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field theories can be recast as a special limit of the refined geometric transition relating open and closed topological string partition functions. We realize the simplest examples of the correspondence explicitly in terms of open-closed geometric transition.
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References
How the literature uses it
6 arXiv papers cite this in 7 sentences
Papers citing it · 5 sentences without a confident label
Cites it as background 2 papers
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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] ).
Gauge/Liouville Triality · M-theory and Large $N$ transitions · 0.94
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Different aspects and applications of the spectral duality can be found in [ref] .
Spectral dualities in XXZ spin chains and five dimensional gauge theories · Introduction · 1.00
What it cites · 70 sentences without a confident label
Builds on 4 papers
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We generalize the exact field theoretic correspondence proposed in [ref] and embed it into the context of refined topological string.
Quantization of Integrable Systems and a 2d/4d Duality · Introduction · 1.00
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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.
A New 2d/4d Duality via Integrability · Nekrasov-Shatashivili limit and Saddle Point Approximation · 0.97
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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] .
Vortex Counting and Lagrangian 3-manifolds · Single Stack of Surface Operators : $n⃗=(0,0, …n_s, …0, 0)$ · 1.00
Uses the method or tool of 4 papers
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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.
Refined BPS state counting from Nekrasov's formula and Macdonald functions · Truncated Partition Function and Surface Operators · 0.90
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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.
Refined Topological Vertex and Instanton Counting · The Closed Refined Topological String · 0.91
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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.
Surface Operator, Bubbling Calabi-Yau and AGT Relation · Open string partition function · 0.95
Compares with 2 papers
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This agrees completely with (3.2) of [ref] .
Refined Topological Vertex and Instanton Counting · The Closed Refined Topological String · 1.00
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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] .].
Surface Operator, Bubbling Calabi-Yau and AGT Relation · Appendix B: Superpotenial from the open string partition function · 0.90
Cites as background 2 papers
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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.
Quantization of Integrable Systems and a 2d/4d Duality · Introduction · 0.82
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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.
A New 2d/4d Duality via Integrability · Introduction · 0.82
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