Alleviating the non-ultralocality of coset sigma-models through a generalized Faddeev-Reshetikhin procedure

作者：Delduc F^*; Magro M; Vicedo B

来源：The Journal of High Energy Physics, 2012, 2012(8): 019.

DOI：10.1007/JHEP08(2012)019

• Lattice Integrable Models
• Integrable Field Theories
• Sigma Models

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 sigma-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.

• 出版日期2012-8