The \(2\times 2\) matrix Schlesinger system and the Belavin-Polyakov-Zamolodchikov system

DOI10.1007/s11232-009-0135-yzbMath1183.81112OpenAlexW2122097824MaRDI QIDQ847892

D. P. Novikov

Publication date: 19 February 2010

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-009-0135-y

zbMATH Keywords

Painlevé equationSchlesinger systemGarnier systemBelavin-Polyakov-Zamolodchikov equation

Mathematics Subject Classification ID

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) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items

Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom ⋮ ``Quantization of an isomonodromic Hamiltonian garnier system with two degrees of freedom ⋮ Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations ⋮ Classical conformal blocks and accessory parameters from isomonodromic deformations ⋮ Generalized Bonnet surfaces and Lax pairs of PVI ⋮ Nearest-neighbour correlation functions for the supersymmetric XYZ spin chain and Painlevé VI ⋮ Symmetries of quantum Lax equations for the Painlevé equations ⋮ The master Painlevé VI heat equation ⋮ Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential ⋮ “Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$ ⋮ Solutions to analogues of non-stationary Schrödinger equations defined by isomonodromic Hamilton system $H^{2+1+1+1}$ ⋮ ``Quantizations of higher Hamiltonian analogues of the Painlevé I and Painlevé II equations with two degrees of freedom ⋮ Conformal field theory of Painlevé VI ⋮ Special polynomials related to the supersymmetric eight-vertex model: a summary ⋮ Quantum Painlevé-Calogero correspondence ⋮ Classical-quantum correspondence and functional relations for Painlevé equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Separation of variables in the Gaudin model
• Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation
• ``Quantizations of the second Painlevé equation and the problem of the equivalence of its \(L-A\) pairs
• Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation
• Infinite conformal symmetry in two-dimensional quantum field theory
• Current algebras and Wess-Zumino model in two dimensions
• Holonomic quantum fields. II: The Riemann-Hilbert problem
• The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem
• Quantization of coset space \(\sigma\)-models coupled to two-dimensional gravity
• On the algebro-geometric integration of the Schlesinger equations
• Canonical structure and symmetries of the Schlesinger equations
• Theta functions and non-linear equations
• EXACT SOLUTIONS OF CONFORMAL FIELD THEORY IN TWO DIMENSIONS AND CRITICAL PHENOMENA
• Grothendieck’s dessins d’enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations

This page was built for publication: The \(2\times 2\) matrix Schlesinger system and the Belavin-Polyakov-Zamolodchikov system