Integrable structure, W-symmetry and AGT relation

V. A. Fateev, A. V. Litvinov

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53 Citations (Scopus)


In these notes we consider integrable structure of the conformal field theory with the algebra of symmetries A = W n H, where W n is W-algebra and H is Heisenberg algebra. We found the system of commuting Integrals of Motion with relatively simple properties. In particular, this system has very simple spectrum and the matrix elements of special primary operators between its eigenstates have nice factorized form coinciding exactly with the contribution of the bifundamental multiplet to the Nekrasov partition function for U(n) gauge theories.

Original languageEnglish
Article number051
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 2012
Externally publishedYes


  • Conformal and W Symmetry
  • Gauge Symmetry
  • Integrable Field Theories


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