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Integrable Structure of Higher Spin CFT and the ODE/IM Correspondence

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arxiv 2405.12636 v2 pith:YXOK4UIF submitted 2024-05-21 hep-th

Sujay K. Ashok , Sanhita Parihar , Tanmoy Sengupta , Adarsh Sudhakar , Roberto Tateo This is my paper
classification hep-th
keywords chargeshigherspinboussinesqquantumconformalconservedcorrespondence
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abstract

We study two dimensional systems with extended conformal symmetry generated by the ${\mathcal W}_3$ algebra. These are expected to have an infinite number of commuting conserved charges, which we refer to as the quantum Boussinesq charges. We compute the eigenvalues of the quantum Boussinesq charges in both the vacuum and first excited states of the higher spin module through the ODE/IM correspondence. By studying the higher spin conformal field theory on the torus, we also calculate thermal correlators involving the energy-momentum tensor and the spin-3 current by making use of the Zhu recursion relations. By combining these results, we show that it is possible to derive the current densities, whose integrals are the quantum Boussinesq charges. We also evaluate the thermal expectation values of the conserved charges, and show that these are quasi-modular differential operators acting on the character of the higher spin module.

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Cited by 5 Pith papers

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

  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 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.

  2. Universal Modular Properties of Generalized Gibbs Ensembles and Chiral Deformations

    hep-th 2026-03 accept novelty 7.0 of 10

    Modular S-transforms of chirally deformed CFT partition functions are determined iteratively by second-order OPE poles of the deforming currents, with explicit multiplicities.

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

    hep-th 2026-04 unverdicted 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. Modular Properties of $\mathcal{W}_3$ Generalised Gibbs Ensembles

    hep-th 2025-08 unverdicted novelty 6.0 of 10

    A proposed asymptotic expansion for the modular S-transform of W_3 generalized Gibbs ensembles with a W_0 charge, supported by Zhu's recursion checks and exact results at c=-2.

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