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The Nekrasov-Shatashvili limit of beta-ensembles with polynomial potential and N=2 supersymmetric gauge theories in the Omega-background is intimately related to complex one-dimensional quantum mechanics.
A. Klemm, W. Lerche and S. Theisen, “Nonperturbative effective actions of N=2 supersymmetric gauge theories,” Int. J. Mod. Phys. A 11
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R. Dijkgraaf and C. Vafa, “Matrix models, topological strings, and supersymmetric gauge theories,” Nucl. Phys. B 644
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R. Dijkgraaf and C. Vafa, “On geometry and matrix models,” Nucl. Phys. B 644
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C. I. Lazaroiu, “Holomorphic matrix models,” JHEP 0305
2003
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A. Klemm, M. Marino and S. Theisen, “Gravitational corrections in supersymmetric gauge theory and matrix models,” JHEP 0303
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J. Zinn-Justin and U. D. Jentschura, “Multi-instantons and exact results I: Conjectures, WKB expansions, and instanton interactions,” Annals Phys. 313
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F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors. “NIST Handbook of Mathematical Functions,” Cambridge University Press, New York, NY, 2010
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D. Krefl and J. Walcher, “Extended Holomorphic Anomaly in Gauge Theory,” Lett. Math. Phys. 95
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2004
Cited alongside, same era.
J. Zinn-Justin and U. D. Jentschura, “Multi-instantons and exact results II: Specific cases, higher-order effects, and numerical calculations,” Annals Phys. 313
2004
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M. Hanada, M. Hayakawa, N. Ishibashi, H. Kawai, T. Kuroki, Y. Matsuo and T. Tada, “Loops versus matrices: The Nonperturbative aspects of noncritical string,” Prog. Theor. Phys. 112
2004
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N. A. Nekrasov, “Seiberg-Witten prepotential from instanton counting,” Adv. Theor. Math. Phys. 7
2004
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R. Flume, F. Fucito, J. F. Morales and R. Poghossian, “Matone’s relation in the presence of gravitational couplings,” JHEP 0404
2004
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V. S. Adamchik, “Symbolic and numeric computations of the Barnes function,” Comp. Phys. Comm. 157 (2004) 181-190
2004
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M. Aganagic, R. Dijkgraaf, A. Klemm, M. Marino and C. Vafa, “Topological strings and integrable hierarchies,” Commun. Math. Phys. 261
2006
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2011
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2011
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2011
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2012
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D. Krefl and J. Walcher, “ABCD of Beta Ensembles and Topological Strings,” JHEP 1211
2012
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J. E. Bourgine, “Large N limit of beta-ensembles and deformed Seiberg-Witten relations,” JHEP 1208
2012
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D. Krefl and A. Schwarz, “Refined Chern-Simons versus Vogel universality,” J. Geom. Phys. 74
2013
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D. Krefl, “Non-Perturbative Quantum Geometry,” JHEP 1402
2014
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