In this talk, I will review the construction of two sigma model type theories and their status as Haag-Kastler nets in the framework of algebraic QFT. The construction of one of them, the O(N) model, is based on inverse scattering and relies on ideas from Haag-Ruelle scattering theory. The O(N,1) model, on the other hand, can be seen as a model for a dS/CFT correspondence. (Joint work with Sabina Alazzawi and Stefan Hollands)