TY - JOUR
T1 - Alleviating the non-ultralocality of coset σ-models through a generalized Faddeev-Reshetikhin procedure
AU - Delduc, F.
AU - Magro, M.
AU - Vicedo, B.
N1 - Published on open access by Springer
PY - 2012/8
Y1 - 2012/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84865085446&partnerID=8YFLogxK
U2 - 10.1007/JHEP08(2012)019
DO - 10.1007/JHEP08(2012)019
M3 - Article
AN - SCOPUS:84865085446
SN - 1126-6708
VL - 2012
JO - Journal of High Energy Physics (JHEP)
JF - Journal of High Energy Physics (JHEP)
IS - 8
M1 - 19
ER -