Painlevé equations from Nakajima-Yoshioka blowup relations

DOI10.1007/s11005-019-01198-4zbMath1428.81127arXiv1811.04050OpenAlexW3105699076MaRDI QIDQ2011171

Mikhail Bershtein, A. I. Shchechkin

Publication date: 28 November 2019

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

Full work available at URL: https://arxiv.org/abs/1811.04050

zbMATH Keywords

\(q\)-difference equationsPainlevé equationsconformal blocksbilinear relationsNekrasov partition functionsblowup relations

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Difference equations, scaling ((q)-differences) (39A13) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Blow-up in context of PDEs (35B44)

Related Items

Quantum spectral problems and isomonodromic deformations, 40 bilinear relations of \(q\)-Painlevé VI from \(\mathcal{N} = 4\) super Chern-Simons theory, 2-parameter \(\tau\)-function for the first Painlevé equation: topological recursion and direct monodromy problem via exact WKB analysis, Blowups in BPS/CFT correspondence, and Painlevé VI, Non-perturbative approaches to the quantum Seiberg-Witten curve, Twisted representations of algebra of \(q\)-difference operators, twisted \(q-W\) algebras and conformal blocks, S-duality and supersymmetry on curved manifolds, Cluster integrable systems and spin chains, On \(q\)-isomonodromic deformations and \(q\)-Nekrasov functions, Blowup relations on \(\mathbb{C}^2/\mathbb{Z}_2\) from Nakajima-Yoshioka blowup relations, BPS quivers of five-dimensional SCFTs, topological strings and \(q\)-Painlevé equations, Combinatorial expressions for the tau functions of \(q\)-Painlevé V and III equations, M2-branes and \({\mathfrak{q}}\)-Painlevé equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions
• Free fermions, \(W\)-algebras, and isomonodromic deformations
• Topological strings from quantum mechanics
• Five-dimensional AGT conjecture and the deformed Virasoro algebra
• Bilinear equations on Painlevé \(\tau\) functions from CFT
• Perverse coherent sheaves on blowup. III: Blow-up formula from wall-crossing
• On determinant representation and integrability of Nekrasov functions
• Instanton counting on blowup. II: \(K\)-theoretic partition function
• \(q\)-Painlevé VI equation arising from \(q\)-UC hierarchy
• Logarithmic extensions of minimal models: characters and modular transformations
• Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
• Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Instanton counting and Chern-Simons theory
• Cluster integrable systems, \(q\)-Painlevé equations and their quantization
• Folding transformations of the Painlevé equations
• Conformal field theory of Painlevé VI
• Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
• Isomonodromic tau-functions from Liouville conformal blocks
• Twisted representations of algebra of \(q\)-difference operators, twisted \(q-W\) algebras and conformal blocks
• Cluster Toda chains and Nekrasov functions
• Quantum curves and \(q\)-deformed Painlevé equations
• Combinatorial expressions for the tau functions of \(q\)-Painlevé V and III equations
• \(K\)-theoretic Donaldson invariants via instanton counting
• Instanton counting on blowup. I: 4-dimensional pure gauge theory
• Fiber-base duality and global symmetry enhancement
• How instanton combinatorics solves Painlevé VI, V and IIIs
• On the Barnes function
• q-deformed Painlevéτfunction andq-deformed conformal blocks
• Bäcklund transformation of Painlevé III(D₈)τfunction
• Quantization conditions and functional equations in ABJ(M) theories
• Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations
• Casorati determinant solutions for theq-difference sixth Painlevé equation
• Extensions of vertex algebras. Constructions and applications
• CFT approach to the q-Painlevé VI equation
• Symplectic fermions