ODE/IM correspondence and the Argyres-Douglas theory

Understand

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.