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Thermal Correlators and Currents of the $\mathcal{W}_3$ Algebra

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arxiv 2410.11748 v1 pith:CEREZBW3 submitted 2024-10-15 hep-th

Sujay K. Ashok , Sanhita Parihar , Tanmoy Sengupta , Adarsh Sudhakar , Roberto Tateo This is my paper
classification hep-th
keywords chargesalgebraconservedhigherspinboussinesqconformalcorrelators
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Two dimensional conformal field theories with the extended $\mathcal{W}_3$ symmetry algebra have an infinite number of mutually commuting conserved charges, which are referred to as the quantum Boussinesq charges. In this work we construct local operators whose zero modes are precisely these conserved charges. For this purpose we study the higher spin conformal field theory on the torus and compute thermal correlators involving the stress tensor and the spin-3 current in a higher spin module of the W3 algebra. In addition we independently obtain the excited state eigenvalues of the quantum Boussinesq charges within the higher spin module via the ODE/IM correspondence. A judicious combination of these data allows us to derive the local operators, whose integrals are the conserved charges of the integrable hierarchy.

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Cited by 4 Pith papers

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

  1. 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.

  2. 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.

  3. 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.

  4. 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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