Strong integrability of $\lambda$-deformed models

TL;DR

This paper establishes the strong integrability of certain lambda-deformed conformal field theories by demonstrating their Lax matrices satisfy Maillet r/s-matrix algebra, revealing underlying symmetries.

Contribution

It proves the strong integrability of lambda-deformed models using Poisson brackets and Maillet algebra, connecting algebraic structures to symmetry properties.

Findings

Lax matrix satisfies Maillet r/s-algebra

Strong integrability is established for lambda-deformed models

Underlying symmetry algebras are recovered at poles of twist functions

Abstract

We study the notion of strong integrability for classically integrable $\lambda$-deformed CFTs and coset CFTs. To achieve this goal we employ the Poisson brackets of the spatial Lax matrix which we prove that it assumes the Maillet $r/s$-matrix algebra. As a consequence the system in question are integrable in the strong sense. Furthermore, we show that the derived Maillet $r/s$-matrix algebras can be realized in terms of twist functions, at the poles of which we recover the underlying symmetry algebras.