Liouville reflection operator, affine Yangian and Bethe ansatz

Alexey Litvinov, Ilya Vilkoviskiy

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8 Citations (Scopus)


In these notes we study integrable structure of conformal field theory by means of Liouville reflection operator/Maulik Okounkov R-matrix. We discuss relation between RLL and current realization of the affine Yangian of gl(1). We construct the family of commuting transfer matrices related to the Intermediate Long Wave hierarchy and derive Bethe ansatz equations for their spectra discovered by Nekrasov and Okounkov and independently by one of the authors. Our derivation mostly follows the one by Feigin, Jimbo, Miwa and Mukhin, but is adapted to the conformal case.

Original languageEnglish
Article number100
JournalJournal of High Energy Physics
Issue number12
Publication statusPublished - Dec 2020


  • Bethe Ansatz
  • Conformal Field Theory


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