TBA equations and WKB periods for higher order ODE

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• Katsushi Ito (Tokyo Institute of Technology)
• Wednesday 14 September 2022, 10:00-11:00
• No Room Required.

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AR2W01 - Physical resurgence: On quantum, gauge, and stringy

We study the WKB periods for the (r+1)-th order ordinary differential equation (ODE) with polynomial potential, which is obtained by conformal limit of the linear problem associated with the A^{(1)}_r affine Toda field equation. The ODE /IM correspondence provides a relation between the Wronskians of the solutions and the Y-functions which satisfy the thermodynamic Bethe ansatz (TBA) equation. We show the equivalence between the logarithm of the Y-functions and the WKB periods, which is confirmed by solving the TBA equation numerically. We also discuss the wall-crossing of the TBA equations from the minimal chamber to the maximal chamber. This talk is based on arXiv:2104.13680[hep-th] and 2111.11047[hep-th] in collaboration with Takayasu Kondo, Kohei Kuroda and Hongfei Shu.

This talk is part of the Isaac Newton Institute Seminar Series series.

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