11th Bologna Workshop on Conformal Field Theory and Integrable Models

Integrals of Motion and ODE/IM correspondence

5 Sept 2025, 09:40

25m

Aula Magna (Dept. of Physics and Astronomy - University of Bologna)

Talk (25 min) Talks

Speaker

Katsushi Ito (Tokyo Institute of Technology)

Description

We study the ODE/IM correspondence between two-dimensional Wg-type conformal field theories and the higher-order ordinary differential equations
(ODEs) obtained from the affine Toda field theories associated with g-type
affine Lie algebras. We calculate the period integrals of the WKB solution to the
ODE along the Pochhammer contour, where the WKB expansions correspond to
the classical conserved currents of the Drinfeld-Sokolov integrable hierarchies. We also compute the integrals of motion for W algebras on a cylinder. Their eigenvalues on the vacuum state are confirmed to agree with the period integrals. These results generalize the ODE/IM correspondence to
higher-order ODEs and can be used to predict higher-order integrals of motion. This talk is based on the paper arXiv:2408.12917 and the joint work with M. Zhu and W. Kono.

Presentation materials

bologna2509.pdf