Wall-crossing of TBA equations and WKB periods for the third order ODE

Autor: Katsushi Ito, Takayasu Kondo, Hongfei Shu
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Nuclear Physics B, Vol 979, Iss , Pp 115788- (2022)
Druh dokumentu: article
ISSN: 0550-3213
DOI: 10.1016/j.nuclphysb.2022.115788
Popis: 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.
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