Opers for higher states of quantum KdV models

DOI10.1007/s00220-020-03792-3zbMath1448.17028arXiv1812.00228OpenAlexW3098351770MaRDI QIDQ778806

Andrea Raimondo, Davide Masoero

Publication date: 20 July 2020

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

Full work available at URL: https://arxiv.org/abs/1812.00228

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items

3D mirror symmetry for instanton moduli spaces, WKB analysis of the linear problem for modified affine Toda field equations, On solutions of the Bethe Ansatz for the Quantum KdV model, \(q\)-opers, \(QQ\)-systems, and Bethe Ansatz, Counting monster potentials, Kondo line defects and affine Gaudin models, Affine opers and conformal affine Toda

Cites Work

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• Integrable structure of quantum field theory: classical flat connections versus quantum stationary states
• Polynomial relations for \(q\)-characters via the ODE/IM correspondence
• Quantization of the Drinfel'd-Sokolov reduction.
• Geometrical loci and cfts via the Virasoro symmetry of the mKdV-SG hierarchy: an excursus
• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case
• Differential equations in the spectral parameter
• Y-system and deformed thermodynamic Bethe Ansatz
• TBA equations and resurgent quantum mechanics
• Formal reduction theory of meromorphic differential equations: a group theoretic view
• Baxter's relations and spectra of quantum integrable models
• A rigid irregular connection on the projective line
• Lie algebras and equations of Korteweg-de Vries type
• Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
• Quantum transfer-matrices for the sausage model
• Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
• Wall-crossing, Hitchin systems, and the WKB approximation
• Quantum sine(h)-Gordon model and classical integrable equations
• Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras
• Poisson pencils: reduction, exactness, and invariants
• Affine Gaudin models and hypergeometric functions on affine opers
• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case
• The Bethe Ansatz and the Tzitz\'eica-Bullough-Dodd equation
• Quantization of soliton systems and Langlands duality
• Asymptotic representations and Drinfeld rational fractions
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• Baxter'sQ-operator for theW-algebraW_N
• Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations
• Lie Group Representations on Polynomial Rings
• Introduction to Lie Algebras and Representation Theory
• The ODE/IM correspondence
• Spectral determinants for Schrödinger equation and \({\mathbb{Q}}\)-operators of conformal field theory
• Integrable structure of \(W_3\) conformal field theory, quantum Boussinesq theory and boundary affine Toda theory