DOI: 10.1007/jhep08(2026)150 ISSN: 1029-8479
The ODE/IM correspondence between C(2)(2)-type linear problems and 2d $$ \mathcal{N} $$ = 1 SCFT
Naozumi Tanabe
A
bstract
We study the ODE/IM correspondence between the linear problem associated with the supersymmetric affine Toda field equation for the twisted affine Lie superalgebra
C
(2)
(2)
=
$$ \mathfrak{osp}{\left(2|2\right)}^{(2)} $$
osp
2
2
2
and two-dimensional
$$ \mathcal{N} $$
N
= 1 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 semi-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
$$ \mathcal{N} $$
N
= 1 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.