Strong integrability of $\lambda$-deformed models

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.

v1:1+22 pages, Latex, v2: NPB version

References in corpus (6)

• An Integrable Deformation of the AdS5 x S5 Superstring
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Integrable flows between exact CFTs
• Assembling integrable sigma-models as affine Gaudin models
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories

Cited by in corpus (1)

• Asymptotics in an Asymptotic CFT