Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case

DOI10.1007/s00220-016-2643-6zbMath1347.82011arXiv1501.07421OpenAlexW1960140160WikidataQ115388575 ScholiaQ115388575MaRDI QIDQ2630721

Daniele Valeri, Davide Masoero, Andrea Raimondo

Publication date: 21 July 2016

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

Full work available at URL: https://arxiv.org/abs/1501.07421

zbMATH Keywords

Lie algebraBethe ansatzaffine Kac-Moody algebras

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Exactly solvable models; Bethe ansatz (82B23)

Related Items (31)

TOROIDAL q-OPERS ⋮ WKB periods for higher order ODE and TBA equations ⋮ Geometric aspects of the ODE/IM correspondence ⋮ Vacuum energy of the Bukhvostov-Lipatov model ⋮ Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers ⋮ Folded quantum integrable models and deformed \(W\)-algebras ⋮ Poisson pencils: reduction, exactness, and invariants ⋮ \(Q\widetilde{Q}\)-systems for twisted quantum affine algebras ⋮ WKB analysis of the linear problem for modified affine Toda field equations ⋮ Geometry and arithmetic of integrable hierarchies of KdV type. I: Integrality ⋮ Affine Gaudin models and hypergeometric functions on affine opers ⋮ \(q\)-opers, \(QQ\)-systems, and Bethe ansatz II: generalized minors ⋮ On solutions of the Bethe Ansatz for the Quantum KdV model ⋮ Deforming the ODE/IM correspondence with \(\mathrm{T}\overline{\mathrm{T}}\) ⋮ Integrable sigma models at RG fixed points: quantisation as affine Gaudin models ⋮ \(q\)-opers, \(QQ\)-systems, and Bethe Ansatz ⋮ ODE/IM correspondence and the Argyres-Douglas theory ⋮ A functor for constructing R$R$‐matrices in the category O$\mathcal {O}$ of Borel quantum loop algebras ⋮ Bukhvostov-Lipatov model and quantum-classical duality ⋮ Oscillator realisations associated to the \(D\)-type Yangian: towards the operatorial Q-system of orthogonal spin chains ⋮ Asymptotic analysis of noisy fitness maximization, applied to metabolism & growth ⋮ Quantum transfer-matrices for the sausage model ⋮ Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case ⋮ Counting monster potentials ⋮ Deformations of \(\mathcal{W}\) algebras via quantum toroidal algebras ⋮ Opers for higher states of quantum KdV models ⋮ Massive ODE/IM correspondence and nonlinear integral equations for ${A_r^{(1)}}$ -type modified affine Toda field equations ⋮ ODE/IM correspondence and supersymmetric affine Toda field equations ⋮ TBA equations for the Schrödinger equation with a regular singularity ⋮ Affine opers and conformal affine Toda ⋮ ODE/IM correspondence for affine Lie algebras: a numerical approach

Uses Software

• GAP

Cites Work

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• Polynomial relations for \(q\)-characters via the ODE/IM correspondence
• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case
• Y-system and deformed thermodynamic Bethe Ansatz
• The mass spectrum and coupling in affine Toda theories.
• Lie algebras and equations of Korteweg-de Vries type
• Integrable structure of conformal field theory. II: \(Q\)-operator and DDV equation
• On the relation between Stokes multipliers and the \(T\)-\(Q\) systems of conformal field theory
• The spectrum of a Coxeter transformation, affine Coxeter transformations, and the defect map
• Higher-level eigenvalues of \(Q\)-operators and Schrödinger equation
• 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
• The asymptotic nature of solutions of linear systems of differential equations
• Differential equations for generalSU(n) Bethe ansatz systems
• The Bethe Ansatz and the Tzitz\'eica-Bullough-Dodd equation
• Quantization of soliton systems and Langlands duality
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• New thermodynamic Bethe ansatz equations without strings
• Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations
• Bethe ansatz equations for the classical $A^{(1)}_{n}$ affine Toda field theories
• 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

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