Large order behavior near the AD point: the case of $\mathcal{N}=2$, $su(2)$, $N_f=2$

Abstract

A non-perturbative effect in $\kappa$ (renormalized string coupling) obtained from the large order behavior in the vicinity of the prototypical Argyres-Douglas critical point of $su(2)$, $N_f=2$, $\mathcal{N}=2$ susy gauge theory can be studied in the GWW unitary matrix model with the log term: the one as the work done against the barrier of the effective potential by a single eigenvalue lifted from the sea and the other as a non-perturbative function contained in the solutions of the nonlinear differential equation PII that goes beyond the asymptotic series. The leading behaviors are of the form $\exp (-\frac{4}{3}\frac{1}{\kappa }(1,{\left(\frac{s}{K}\right)}^{\frac{3}{2}}))$ respectively. We make comments on their agreement.

14 pages