Appears in collection : Marco Serone : Resurgence in Integrable Field Theories

We review recent progress in understanding the resurgent properties of integrable field theories in two dimensions. After a brief recap on elementary notions about Borel resummations, we start with a quick historical detour on the study of the large order behaviour of perturbation theory in quantum field theory (QFT) before the advent of resurgence. We then introduce basic notions of resurgence and apply it on three well-known integrable field theories which are UV-free, develop a mass gap in the IR, admit a 1/N expansion, and present the so called renormalon singularities. The interplay between resurgent properties and the 1/N expansion is discussed. The observable of interest is the free energy in the presence of a chemical potential coupled to a conserved charge, which can be computed exactly with thermodynamic Bethe ansatz techniques and/or large N QFT methods. Results at finite N will also be reviewed.