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Journal of High Energy Physics

, 2019:60 | Cite as

Argyres-Douglas theories, Painlevé II and quantum mechanics

  • Alba Grassi
  • Jie GuEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We show in details that the all order genus expansion of the two-cut Hermitian cubic matrix model reproduces the perturbative expansion of the H1 Argyres-Douglas theory coupled to the Ω background. In the self-dual limit we use the Painlevé/gauge correspondence and we show that, after summing over all instanton sectors, the two-cut cubic matrix model computes the tau function of Painlevé II without taking any double scaling limit or adding any external fields. We decode such solution within the context of transseries. Finally in the Nekrasov-Shatashvili limit we connect the H1 and the H0 Argyres-Douglas theories to the quantum mechanical models with cubic and double well potentials.

Keywords

Matrix Models Supersymmetric Gauge Theory Conformal Field Theory Integrable Hierarchies 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Simons Center for Geometry and PhysicsSUNYStony BrookU.S.A.
  2. 2.Laboratoire de Physique Théorique de l’ École Normale Supérieure, CNRS, PSL Research University, Sorbonne Universités, UPMCParisFrance

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