The ODE/IM Correspondence between $C(2)^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT
Abstract
We study the ODE/IM correspondence between the linear problem associated with the supersymmetric affine Toda field equation for the twisted affine Lie superalgebra and two-dimensional superconformal field theories (SCFTs). On the ODE side, we introduce a boundary condition more suitable for the conformal limit and the subsequent WKB analysis and diagonalize the resulting Lax operator. This leads to a WKB expansion from which we extract the WKB periods and non-local conserved quantities up to tenth order. On the IM side, we compute the eigenvalues of the local integrals of motion on the cylinder in both the Neveu-Schwarz and Ramond sectors of 2d SCFTs. We then compare the two sides and verify, up to sixth order, that the WKB periods coincide with the eigenvalues of the local integrals of motion for highest-weight states in the Neveu-Schwarz sector.
Cite
@article{arxiv.2604.14899,
title = {The ODE/IM Correspondence between $C(2)^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT},
author = {Naozumi Tanabe},
journal= {arXiv preprint arXiv:2604.14899},
year = {2026}
}