KNIZHNIK–ZAMOLODCHIKOV–BERNARD EQUATIONS CONNECTED WITH THE EIGHT-VERTEX MODEL

1998/04/15 by H. Babujian, A. Lima-Santos, Rubik Poghossian +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #cond-mat.stat-mech #hep-th #nlin.SI #solv-int

paper · pdf · doi:10.1142/s0217751x99000300

published as Int. Journ. Mod. Phys. A14 (1999) 615-630 · 20 pages latex, macro: tcilatex

arxiv created 1998/04/15 · openalex publication_date 1999/02/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By the use of the quasiclassical limit of Baxter's eight-vertex R matrix, an elliptic generalization of the Knizhnik–Zamolodchikov equation is constructed. An integral representation for the solution of this equation is obtained via the off-shell Bethe ansatz. It is shown that there exists a gauge transformation connecting this equation with the Knizhnik–Zamolodchikov–Bernard equation for the SU(2) WZNW model on a torus.

Citations

• Algebraic bethe ansatz for the XYZ Gaudin model
• Current algebra and Wess-Zumino model in two dimensions
• Infinite conformal symmetry in two-dimensional quantum field theory
• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. II. Equivalence to a generalized ice-type lattice model

Cited by

• Elliptic Gaudin models and elliptic KZ equations
• sl(2|1)(2) Gaudin magnet and its associated Knizhnik–Zamolodchikov equation