Large Order Behavior Near the AD Point: The Case of 𝒩 = 2, (2), = 2 Toda theories, matrix models, topological strings, and N=2 gauge systems A study of U(N) lattice gauge theory in 2-dimensions The strength of nonperturbative effects in string theory Cubic pencils and Painlevé Hamiltonians The annular report on non-critical string theory
Chuan-Tsung Chan (Department of Applied Physics, Tunghai University, Taichung, 40704, Taiwan); H Itoyama (Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan, Osaka Central Advanced Mathematical Institute (OCAMI), Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan); R Yoshioka (Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan, Osaka Central Advanced Mathematical Institute (OCAMI), Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan)
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), N$_{f}$ = 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 . We make comments on their agreement.
