Large order behavior near the AD point: the case of N = 2 , su(2), Nf = 2

Abstract

A non-perturbative effect in κ (renormalized string coupling) obtained from the large order behavior in the vicinity of the prototypical Argyres-Douglas critical point of su(2), Nf = 2, $0\mathcal {N} =2$ 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.