Treating divergent perturbation theory: Lessons from exactly solvable 2D models at large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>

We consider the operator product expansion (OPE) of correlation functions in supersymmetric $O(N)$ non-linear sigma model at sub-leading order large $N$ limit to study cancellation between ambiguities coming from infrared renormalons and those various operators OPE. As has been discussed context Yang-Mills theory four dimensions, supersymmetry presents a challenge this cancellation. In bid solve problem we as toy model. A background field method inspired by Polyakov's treatment renormalization bosonic is used identify explicit OPE two-point fermionic fields coefficient OPE, exact are expanded powers natural length scale. The arising vacuum expectation values shown cancel all orders. question without matter remains open.