Integrable structure, W-symmetry and AGT relation

  • V. A. Fateev
  • A. V. LitvinovEmail author
Open Access


In these notes we consider integrable structure of the conformal field theory with the algebra of symmetries \( \mathcal{A} = {W_n} \otimes H \), 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.


Gauge Symmetry Conformal and W Symmetry Integrable Field Theories 


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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsMoscow RegionRussia
  2. 2.Laboratoire Charles Coulomb, L2C, UMR 5221Université Montpellier IIMontpellierFrance
  3. 3.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.

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