Abstract
The Faddeev-Reshetikhin procedure corresponds to a removal of the non-ultralocality of the classical SU(2) principal chiral model. It is realized by defining another field theory, which has the same Lax pair and equations of motion but a different Poisson structure and Hamiltonian. Following earlier work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible to alleviate in a similar way the non-ultralocality of symmetric space σ-models. The equivalence of the equations of motion holds only at the level of the Pohlmeyer reduction of these models, which corresponds to symmetric space sine-Gordon models. This work therefore shows indirectly that symmetric space sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an integrable potential, have a mild non-ultralocality. The first step needed to construct an integrable discretization of these models is performed by determining the discrete analogue of the Poisson algebra of their Lax matrices.
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Delduc, F., Magro, M. & Vicedo, B. Alleviating the non-ultralocality of coset σ-models through a generalized Faddeev-Reshetikhin procedure. J. High Energ. Phys. 2012, 19 (2012). https://doi.org/10.1007/JHEP08(2012)019
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DOI: https://doi.org/10.1007/JHEP08(2012)019