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arXiv · 2402.03670

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

Chuan-Tsung Chan·Hiroshi Itoyama·Reiji Yoshioka
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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.

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Chuan-Tsung Chan, Hiroshi Itoyama, Reiji Yoshioka. 2024-02-06. Large order behavior near the AD point: the case of $\mathcal{N} =2$, $su(2)$, $N_f =2$. https://arxiv.org/abs/2402.03670

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