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

TL;DR

This paper extends the Faddeev-Reshetikhin procedure to symmetric space sigma models, reducing their non-ultralocality and paving the way for integrable discretizations by analyzing their Poisson structures.

Contribution

It generalizes the Faddeev-Reshetikhin method to symmetric space sigma models, showing how to alleviate non-ultralocality and establishing a basis for discretization.

Findings

Non-ultralocality of symmetric space sigma models can be alleviated.

The Poisson algebra of Lax matrices for these models can be discretized.

Symmetric space sine-Gordon models have mild non-ultralocality.

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 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.