Non-perturbative large N trans-series for the Gross-Witten-Wadia beta function

We describe the non-perturbative trans-series, at both weak- and strong-coupling, of the large N approximation to the beta function of the Gross-Witten-Wadia unitary matrix model. This system models a running coupling, and the structure of the trans-series changes as one crosses the large N phase transition. The perturbative beta function acquires a non-perturbative trans-series completion at large but finite N in the 't Hooft limit, as does the running coupling.