ODE/IM correspondence and the Argyres-Douglas theory

TL;DR

This paper explores the quantum spectral curves of Argyres-Douglas theories using the ODE/IM correspondence, revealing their connection to non-unitary coset models and analyzing quantum periods through WKB methods.

Contribution

It identifies the specific integrable models associated with Argyres-Douglas theories and clarifies the relation between Y-functions and quantum periods using WKB analysis.

Findings

Models for A_{2N}-type theories are non-unitary coset models at fractional levels.

Established the relation between Y-functions and quantum periods.

Analyzed quantum spectral curves for D and E type theories.

Abstract

We study the quantum spectral curve of the Argyres-Douglas theories in the Nekrasov-Sahashvili limit of the Omega-background. Using the ODE/IM correspondence we investigate the quantum integrable model corresponding to the quantum spectral curve. We show that the models for the $A_{2N}$-type theories are non-unitary coset models $(A_1)_1\times (A_1)_{L}/(A_1)_{L+1}$ at the fractional level $L=\frac{2}{2N+1}-2$, which appear in the study of the 4d/2d correspondence of ${\cal N}=2$ superconformal field theories. Based on the WKB analysis, we clarify the relation between the Y-functions and the quantum periods and study the exact Bohr-Sommerfeld quantization condition for the quantum periods. We also discuss the quantum spectral curves for the D and E type theories.