Journal of High Energy Physics

, 2012:36 | Cite as

Parafermionic Liouville field theory and instantons on ALE spaces

  • M. N. Alfimov
  • G. M. Tarnopolsky


In this paper we study the correspondence between the \( \widehat{\text{su}}{(n)_k} \oplus \widehat{\text{su}}{(n)_p}/\widehat{\text{su}}{(n)_{{k + p}}} \) coset conformal field theories and \( \mathcal{N} = {2} \) SU(n) gauge theories on \( {\mathbb{R}^4}/{\mathbb{Z}_p} \). Namely we check the correspondence between the SU(2) Nekrasov partition function on \( {\mathbb{R}^4}/{\mathbb{Z}_4} \) and the conformal blocks of the S 3 parafermion algebra (in S and D modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on \( {\mathbb{R}^4}/{\mathbb{Z}_p} \) we also find some evidence that this correspondence with arbitrary p takes place up to the U(1)-factor.


Supersymmetric gauge theory Conformal and W Symmetry 


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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.P.N. Lebedev Physical InstituteMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.Landau Institute for Theoretical PhysicsChernogolovkaRussia

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