Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and higher rank trigonometric Landau-Lifshitz model
- Resource Type
- Working Paper
- Authors
- Atalikov, K.; Zotov, A.
- Source
- Subject
- High Energy Physics - Theory
Mathematical Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems
- Language
We consider the classical integrable 1+1 trigonometric ${\rm gl}_N$ Landau-Lifshitz models constructed by means of quantum $R$-matrices satisfying also the associative Yang-Baxter equation. It is shown that 1+1 field analogue of the trigonometric Calogero-Moser-Sutherland model is gauge equivalent to the Landau-Lifshitz model, which arises from the Antonov-Hasegawa-Zabrodin trigonometric non-standard $R$-matrix. The latter generalizes the Cherednik's 7-vertex $R$-matrix in ${\rm GL}_2$ case to the case of ${\rm GL}_N$. Explicit change of variables between the 1+1 models is obtained.
Comment: 16 pages