Irregular conformal blocks and connection formulae for Painlevé V functions

DOI10.1063/1.5031841zbMath1404.33020arXiv1806.08344OpenAlexW2808754339MaRDI QIDQ4687688

Julien Roussillon, Hajime Nagoya, Oleg Lisovyy

Publication date: 12 October 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.08344

zbMATH Keywords

monodromyPainlevé transcendentsFredholm determinantToeplitz determinantVirasoro algebraLax pairtau functionVerma moduleStokes matricesYoung diagramsWhittaker functionsNekrasov functionsWhittaker moduleWhittaker vectorsconnection formulasconnection problemBarnes \(G\)-functionconnection constantsconformal field theory (CFT)Jimbo-Miwa-Ueno tau functionStokes sectorsVirasoro generatorsquantum dilogarithmsRiemann-Hilbert problem (RHP)Virasoro conformal blocksWeyl symmetry group4D supersymmetric gauge theoryAlday-Gaiotto-Tachikawa (AGT) relationChiral vertex operatorirregular conformal blocksPonsot-Teschner Formularegular conformal blocksSzegő constant

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Fredholm structures on infinite-dimensional manifolds (58B15) Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Riemann-Hilbert problems in context of PDEs (35Q15) Asymptotic expansions of solutions to ordinary differential equations (34E05) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40) Monodromy on manifolds (58K10) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Painlevé-type functions (33E17) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

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