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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.14899 |
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| _version_ | 1866913050452295680 |
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| author | Tanabe, Naozumi |
| author_facet | Tanabe, Naozumi |
| contents | We study the ODE/IM correspondence between the linear problem associated with the supersymmetric affine Toda field equation for the twisted affine Lie superalgebra $C(2)^{(2)} = \mathfrak{osp}(2|2)^{(2)}$ and two-dimensional $\mathcal{N}=1$ 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 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 $\mathcal{N}=1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14899 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The ODE/IM Correspondence between $C(2)^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT Tanabe, Naozumi High Energy Physics - Theory Mathematical Physics We study the ODE/IM correspondence between the linear problem associated with the supersymmetric affine Toda field equation for the twisted affine Lie superalgebra $C(2)^{(2)} = \mathfrak{osp}(2|2)^{(2)}$ and two-dimensional $\mathcal{N}=1$ 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 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 $\mathcal{N}=1$ 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. |
| title | The ODE/IM Correspondence between $C(2)^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.14899 |