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Integrals of motion in conformal field theory with W-symmetry and the ODE/IM correspondence

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arxiv 2408.12917 v2 pith:ISZH7YAW submitted 2024-08-23 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords integralscorrespondencefieldhigher-ordermotionaffinealgebrasconformal
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study the ODE/IM correspondence between two-dimensional $WA_{r}$/$WD_{r}$-type conformal field theories and the higher-order ordinary differential equations (ODEs) obtained from the affine Toda field theories associated with $A_r^{(1)}/D_r^{(1)}$-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 $WA_{r}$($WD_{r}$) algebras on a cylinder. Their eigenvalues on the vacuum state are confirmed to agree with the period integrals up to the sixth order. These results generalize the ODE/IM correspondence to higher-order ODEs and can be used to predict higher-order integrals of motion.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The ODE/IM Correspondence between $C(2)^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT

    hep-th 2026-04 unverdicted novelty 7.0 of 10

    WKB periods from the C(2)^{(2)} linear problem match eigenvalues of local integrals of motion in the Neveu-Schwarz sector of 2d N=1 SCFTs up to sixth order.

  2. Integrals of motion in $WE_6$ CFT and the ODE/IM correspondence

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    Period integrals from the E6 ODE WKB expansion match eigenvalues of WE6 CFT integrals of motion up to sixth order.

  3. Integrals of motion in $WE_6$ CFT and the ODE/IM correspondence

    hep-th 2026-04 conditional novelty 6.0 of 10

    The WKB periods of the E_6^(1) linear problem agree with the integrals of motion of the W E6 CFT on highest-weight states up to spin 6 under the standard parameter dictionary.

  4. On W-algebras and ODE/IM correspondence

    hep-th 2025-08 conditional novelty 6.0 of 10

    The eigenvalues of quantum KdV-type charges in Virasoro, W3, and W4 algebras are computed from Bethe roots via WKB periods of Catalan curves, verified against direct CFT diagonalization.

  5. The ODE/IM Correspondence between $C(2)^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT

    hep-th 2026-04 accept novelty 5.5 of 10

    WKB periods of the fully diagonalized C(2)^{(2)} Lax operator coincide with NS-sector local IoM eigenvalues of N=1 SCFT up to sixth order under a fixed parameter dictionary.

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