The classical Yang–Baxter equation and the associated Yangian symmetry of gauged WZW-type theories

Abstract

We construct the Lax-pair, the classical monodromy matrix and the corresponding solution of the Yang-Baxter equation, for a two-parameter deformation of the Principal chiral model for a simple group. This deformation includes as a one-parameter subset, a class of integrable gauged WZW-type theories interpolating between the WZW model and the non-Abelian T-dual of the principal chiral model. We derive in full detail the Yangian algebra using two independent methods: by computing the algebra of the non-local charges and alternatively through an expansion of the Maillet brackets for the monodromy matrix. As a byproduct, we also provide a detailed general proof of the Serre relations for the Yangian symmetry.Dedicated to the memory of Sotirios Bonanos whose MATHEMATICA software has helped numerous researchers

Integrable flows between exact CFTs

“…(3.23) and (3.24) of [52]) provided that the Poisson brackets of Lσ assume the Maillet form and the modified Yang-Baxter equation is satisfied. Our effective action (2.12) implies a canonical structure which is precisely a double copy of the two-parameter deformation of the PCM's canonical structure presented in [53]. In this work it was shown that the Maillet brackets are satisfied and an explicit solution to the modified classical Yang-Baxter equation was found (see section 3, where the parameter ρ in there is related to the level asymmetry as in eq.…”

Strong integrability of λ-deformed models

“…In this section we work out the r/s-Maillet form for the isotropic group case at equal and unequal levels. In the equal level case, we review the construction in [8] as a warm up for the unequal level case.…”

“…Then we express L 1 or equivalently A i|1 , B ± in terms of J i± . 8 We are in position to compute the Poisson brackets of L 1 and for simplicity we start with the equal level case.…”

Yang-Baxter deformations and string dualities

“…For an earlier attempt to study higher-dimensional cases, see [19]. For integrable deformations of Wess-Zumino-Novikov-Witten models, see [20][21][22][23][24][25][26].…”