Non-perturbative effects and infrared renormalons within the 1/N expansion of the O(N) non-linear sigma model

We analyze the structure of the Borel transform of the two-dimensional O(N) non-linear σ model within its $\text{1}\text{N}$ expansion. We check the existence of IR singularities (IR renormalons) and the presence of non-perturbative terms which organize themselves in an operator expansion à la Shifman-Vainshtein-Zakharov. We prove that renormalons cancel between the different terms of the operator expansion, so that there is a well-defined resummation procedure of the perturbative series. We suggest that this mechanism provides a general solution of the IR renormalons problem for massless UV free field theories.