Abstract
We prove the conjecture of Sfetsos, Siampos and Thompson that suitable analytic continuations of the Poisson-Lie T-duals of the bi-Yang-Baxter sigma models coincide with the recently introduced generalized lambda models. We then generalize this result by showing that the analytic continuation of a generic sigma model of "universal WZW-type" introduced by Tseytlin in 1993 is nothing but the Poisson-Lie T-dual of a generic Poisson-Lie symmetric sigma model introduced by Klimcik and Severa in 1995.
Highlights
Two kinds of integrable nonlinear σ-models, the so-called η-deformation of the principal chiral model [1, 2] and the λ-deformation of the WZW model [3], have recently attracted much attention because of their relevance in string theory or in non-commutative geometry [4]. The integrability of those models was proven at the level of the Lax pair in [2, 3] and at the level of the so called r/s exchange relations in [5]. Both the η-model and the λ-model turned out to be deformable further to give rise to several families of multi-parametric integrable σ-models1 [6, 7, 8] living on general semi-simple group targets
In three recent papers [11], [12] and [8], there was suggested that the ηdeformation of the principal chiral model [1, 2] and the λ-deformation of the WZW model should be related by the Poisson-Lie T-duality [13, 14] followed by an appropriate analytic continuation of the geometry of the λ-model target
Such suggestion was fully worked out for the simplest group target SU(2) in [8] where it was shown that the Poisson-Lie T-dual of the biYang-Baxter model [7] coincides with the analytically continued generalized λ-model [8]
Summary
Physics Letters B, Elsevier, 2016, 760, pp.345 - 349. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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