Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations

Abstract

We generalize the previously established connection between the off-shell Bethe ansatz equation for inhomogeneous SU(2) lattice vertex models in the quasiclassical limit and the solutions of the SU(2) Knizhnik-Zamolodchikov equations to the case of arbitrary simple Lie algebras.

10 pages (LaTeX), BONN-HE-93-30, YPI 1407 (18)-93

Cited by in corpus (58)

• Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
• Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz
• Exact form factors in integrable quantum field theories: the sine-Gordon model (II)
• Large N limit of the exactly solvable BCS model: analytics versus numerics
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Algebraic Bethe Ansatz for a discrete-state BCS pairing model
• Integrable models for confined fermions: applications to metallic grains
• Chern-Simons theory and BCS superconductivity
• Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets
• The BCS model and the off shell Bethe ansatz for vertex models
• Worldsheet Form Factors in AdS/CFT
• Electrostatic analogy for integrable pairing force Hamiltonians
• BPS States in Omega Background and Integrability
• Resolution of the Nested Hierarchy for Rational sl(n) Models
• Bethe Ansatz solution for quantum spin-1 chains with boundary terms
• The open XXZ and associated models at q root of unity
• Creation operators and Bethe vectors of the osp(1|2) Gaudin model
• Trigonometric osp(1|2) Gaudin model
• Bethe Ansatze for 19-vertex Models
• Limits of Gaudin algebras, quantization of bending flows, Jucys--Murphy elements and Gelfand--Tsetlin bases
• Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields
• U(N) Matrix Difference Equations and a Nested Bethe Ansatz
• Quantum Integrable Model of an Arrangement of Hyperplanes
• Gaudin models for gl(m|n)
• Comments on World-Sheet Form Factors in AdS/CFT
• Yang-Baxter equation and reflection equations in integrable models
• sl_2 Gaudin model with Jordanian twist
• Off-Shell Bethe Ansatz Equation for $osp(2|1)$ Gaudin Magnets
• Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model
• Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
• Trigonometric sl(2) Gaudin model with boundary terms
• Cyclotomic Gaudin models: construction and Bethe ansatz
• An Algebraic Approach to Form Factors
• Boundary Wess-Zumino-Novikov-Witten Model from the Pairing Hamiltonian
• $sl(2|1{)}^{(2)}$ Gaudin Magnet and its associated Knizhnik-Zamolodchikov equation
• Algebraic Bethe ansatz for U(1) Invariant Integrable Models: Compact and non-Compact Applications
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Singular and non-singular eigenvectors for the Gaudin model
• Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors
• Functional relations and the Yang-Baxter algebra
• Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations
• Exactly solvable discrete BCS - type Hamiltonians and the Six-Vertex model
• Surface energy of the one-dimensional supersymmetric $t-J$ model with unparallel boundary fields
• Algebraic Bethe Ansatz for deformed Gaudin model
• Gaudin magnet with impurity and its generalized Knizhnik-Zamolodchikov equation
• The elementary excitations of the BCS model in the canonical ensemble
• Confluent KZ equations for sl_N with Poincare rank 2 at infinity
• Yang-Baxter Algebra for the n-Harmonic Oscillator Realisation of sp(2n,R)
• Jordanian deformation of the open sl(2) Gaudin model
• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models
• $A_2^{(2)}$ Gaudin model and its associated Knizhnik-Zamolodchikov equation
• Osp(1|2) Off-shell Bethe Ansatz Equations
• Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebras
• $osp(1|2)$ off-shell Bethe ansatz equation with boundary terms
• On the algebraic Bethe ansatz: Periodic boundary conditions
• Quadratic and cubic Gaudin Hamiltonians and super Knizhnik-Zamolodchikov equations for general linear Lie superalgebras
• On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model
• On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain