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

Georgios Itsios (Department of Mathematics, University of Patras, Patras, 26110, Greece) ; Konstantinos Sfetsos (Department of Nuclear and Particle Physics, Faculty of Physics, University of Athens, Athens, 15771, Greece) ; Konstantinos Siampos (Mécanique et Gravitation, Université de Mons, Mons, 7000, Belgium) ; Alessandro Torrielli (Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK)

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.

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Published on:
09 October 2014
Publisher:
Elsevier
Published in:
Nuclear Physics B (2014)

Pages 64-86
DOI:
https://doi.org/10.1016/j.nuclphysb.2014.10.004
Copyrights:
The Authors
Licence:
CC-BY-3.0

Fulltext files: