Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and higher rank trigonometric Landau-Lifshitz model

Abstract

We consider the classical integrable 1+1 trigonometric ${\mathrm{gl}}_N$ 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 ${\mathrm{GL}}_2$ case to the case of ${\mathrm{GL}}_N$. Explicit change of variables between the 1+1 models is obtained.

16 pages

References in corpus (5)

• Relativistic Classical Integrable Tops and Quantum R-matrices
• Field analogue of the Ruijsenaars-Schneider model
• Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations
• Higher rank 1+1 integrable Landau-Lifshitz field theories from associative Yang-Baxter equation
• Gauge equivalence between 1+1 rational Calogero-Moser field theory and higher rank Landau-Lifshitz equation

Cited by in corpus (2)

• Non-ultralocal classical r-matrix structure for 1+1 field analogue of elliptic Calogero-Moser model
• On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion