Elliptic Gaudin models and elliptic KZ equations

2001/10/27 by M. D. Gould, Mark D. Gould, Yao-Zhong Zhang +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Face (sociological concept) #Geology #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Philosophy #Physics #Pure mathematics #Type (biology) #cond-mat #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1016/s0550-3213(02)00136-0

published as Nucl.Phys. B630 (2002) 492-508 · LaTex file 18 pages; Errors corrected and references added

arxiv created 2001/10/27 · openalex publication_date 2002/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik-Zamolodchikov equations and their solutions are given.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• Algebraic bethe ansatz for the XYZ Gaudin model
• Integrable XYZ Spin Chain with Boundaries
• Current algebra and Wess-Zumino model in two dimensions
• Diagonalisation d'une classe d'hamiltoniens de spin
• Gaudin model, Bethe Ansatz and critical level
• Boundary conditions for integrable quantum systems
• KNIZHNIK–ZAMOLODCHIKOV–BERNARD EQUATIONS CONNECTED WITH THE EIGHT-VERTEX MODEL