Integrable Non-linear Sigma Models in (1+1)-Dimensions

Abstract

This chapter will introduce the notion of classical integrability of non-linear sigma models in two dimensions. In general, non-linear sigma models are not classically integrable in general dimensions and even in two dimensions. However, there are well-known integrable examples in two dimensions such as principal chiral model and symmetric coset sigma model. Here for these two examples, the classical integrability will be described by explicitly presenting a classical Lax pair and the associated infinite-dimensional algebra, Yangian.