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arXiv · 1707.03596

ODE/IM correspondence and the Argyres-Douglas theory

Katsushi Ito·Hongfei Shu
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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.

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Katsushi Ito, Hongfei Shu. 2017-07-12. ODE/IM correspondence and the Argyres-Douglas theory. https://doi.org/10.1007/jhep08(2017)071

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