| Summary: | We study the WKB periods for the third order ordinary differential equation (ODE) with polynomial potential, which is obtained by the Nekrasov-Shatashvili limit of (A2,AN) Argyres-Douglas theory in the Omega background. In the minimal chamber of the moduli space, we derive the Y-system and the thermodynamic Bethe ansatz (TBA) equations by using the ODE/IM correspondence. The exact WKB periods are identified with the Y-functions. Varying the moduli parameters of the potential, the wall-crossing of the TBA equations occurs. We study the process of the wall-crossing from the minimal chamber to the maximal chamber for (A2,A2) and (A2,A3). When the potential is a monomial type, we show the TBA equations obtained from the (A2,A2) and (A2,A3)-type ODE lead to the D4 and E6-type TBA equations respectively.
|
|---|