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 \({\rm gl}_N\) 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.