Speaker
Description
We study the WKB periods for the $(r+1)$-th order ordinary differential equation (ODE) with polynomial potential which is obtained by the Nekrasov-Shatashvili limit of $(A_r, A_N)$ Argyres-Douglas theory in Omega background. We derive the thermodynamic Bethe ansatz (TBA) equations governing the exact WKB periods, which provides a generalization of the ODE/IM correspondence. Varying the moduli space parameters of the potential, one observes the wall-crossing of the TBA equations. When the potential is monomimal type, we show the TBA equations obtained from the $(A_2, A_2)$ and $(A_2, A_3)$-type ODE lead to the $D_4$ and $E_6$-type TBA equations respectively. This talk is based on the work (hep-th/2104.13680) in collaboration with Katsushi Ito, Takayasu Kondo and Kohei Kuroda and the work in progress.
