Large Order Behavior Near the AD Point: The Case of 𝒩 = 2, su(2), Nf = 2

Abstract

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, $\mathcal {N} =2$ supersymmetric gauge theory can be studied in the Gross–Witten–Wadia unitary matrix model with the log term: 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 Painlevé II equation that goes beyond the asymptotic series. The leading behaviors are of the form $\exp \{[-({4}/{3})({1}/{\kappa })] \, [1, \left({s}/{K}\right)^{{3}/{2}}]\}$. We make comments on their agreement.