Quasiclassical asymptotics of solutions to the KZ equations

Abstract

The quasiclassical asymptotics of the Knizhnik-Zamolodchikov system is studied. Solutions to this system in this limit are related naturally to Bethe vectors in the Gaudin model of spin chains.

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Cited by in corpus (69)

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• KZ Characteristic Variety as the Zero Set of Classical Calogero-Moser Hamiltonians
• Critical points and resonance of hyperplane arrangements
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• Asymptotic Solutions to the Knizhnik-Zamolodchikov Equation and Crystal Base
• Quantum Integrable Model of an Arrangement of Hyperplanes
• Gaudin models for gl(m|n)
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• sl_2 Gaudin model with Jordanian twist
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• The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
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• q-Opers, QQ-Systems, and Bethe Ansatz
• Exact out-of-equilibrium central spin dynamics from integrability
• Trigonometric sl(2) Gaudin model with boundary terms
• Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
• Algebraic nested Bethe ansatz for the elliptic Ruijsenaars model
• Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems
• Bases of Bethe Vectors and Difference Equations with Regular Singular Points
• A theorem of Heine-Stieltjes, the Wronski map, and Bethe vectors in the sl_p Gaudin model
• Gaudin model and opers
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• Bispectral and $(\glN,\glM)$ Dualities
• Self-duality of the SL_2 Hitchin integrable system at genus two
• Opers on the projective line, flag manifolds and Bethe Ansatz
• Singular and non-singular eigenvectors for the Gaudin model
• Cyclotomic Gaudin models with irregular singularities
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• On the Gaudin model associated to Lie algebras of classical types
• Intersections of Schubert varieties and highest weight vectors in tensor products of sl_{N+1}-representations
• Algebraic Bethe Ansatz for deformed Gaudin model
• Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory
• FQHE and $t{t}^{\ast }$ geometry
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• Resonant local systems on complements of discriminantal arrangements and sl_2 representations
• Bethe algebra and algebra of functions on the space of differential operators of order two with polynomial solutions
• Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model
• Remarks on critical points of phase functions and norms of Bethe vectors
• $A_2^{(2)}$ Gaudin model and its associated Knizhnik-Zamolodchikov equation
• Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz
• Jordanian deformation of the open sl(2) Gaudin model
• Asymptotic solutions to the sl_2 KZ equation and the intersection of Schubert classes
• Difference Operators and Duality for Trigonometric Gaudin and Dynamical Hamiltonians
• Critical points of master functions and the mKdV hierarchy of type A^2_2
• On the Gaudin model of type G${}_2$
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• Quantum Analytic Langlands Correspondence
• Critical points of functions, sl_2 representations, and Fuchsian differential equations with only univalued solutions
• New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case
• Norm of a Bethe Vector and the Hessian of the Master Function
• Populations of Solutions to Cyclotomic Bethe Equations
• A Bethe Ansatz for Symmetric Groups
• On Bethe vectors in the sl_{N+1} Gaudin model
• Interrelations between dualities in classical integrable systems and classical-classical version of quantum-classical duality
• Higher Lame Equations and Critical Points of Master Functions
• Gaudin's model and the generating function of the Wronski map
• Higher spin polynomial solutions of quantum Knizhnik--Zamolodchikov equation
• Yang-Yang functions, Monodromy and knot polynomials
• Rational functions with prescribed critical points
• Labelling Schubert intersections in the Grassmanian
• Exact solutions for some sigma models in quantum field theory