Spectrum of quantum KdV hierarchy in the semiclassical limit

Anatoly Dymarsky, Ashish Kakkar, Kirill Pavlenko, Sotaro Sugishita

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central charge c. Classically, KdV charges Q2n−1 generate completely integrable dynamics on the co-adjoint orbit of the Virasoro algebra. They can be expressed in terms of action variables Ik, e.g. as a power series expansion. Quantum-mechanically this series becomes the expansion in 1/c, while action variables become integer-valued quantum numbers ni. Crucially, classical expression, which is homogeneous in Ik, acquires quantum corrections that include terms of subleading powers in nk. At first two non-trivial orders in 1/c expansion these “quantum” terms can be fixed from the analytic form of Q2n−1 acting on the primary states. In this way we find explicit expression for the spectrum of Q2n−1 up to first three orders in 1/c expansion. We apply this result to study thermal expectation values of Q2n−1 and free energy of the KdV Generalized Gibbs Ensemble.

Original languageEnglish
Article number169
JournalJournal of High Energy Physics
Issue number9
StatePublished - Sep 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).


  • Conformal Field Models in String Theory
  • Conformal and W Symmetry
  • Integrable Field Theories

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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