Classical integrability in Lie algebra expanded coset sigma models

In this talk I will present my recent work arXiv:2005.01736 in collaboration with L. Romano. I will recall the technique of Lie algebra expansion and I will show how to apply it to the global symmetry of a string coset sigma model in order to systematically generate new sigma models. The main result will be a set of criteria for the existence of a Lax pair for these new models, which proves classical integrability. In the last part of the talk I will discuss how this result connects to non-relativistic string theory.