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Parafermionic Liouville field theory and instantons on ALE spaces

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Abstract

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.

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Authors and Affiliations

  1. P.N. Lebedev Physical Institute, Leninskiy pr. 53, 119991, Moscow, Russia

    M. N. Alfimov

  2. Moscow Institute of Physics and Technology, Institutskiy per. 9, 141700, Dolgoprudny, Russia

    M. N. Alfimov

  3. Landau Institute for Theoretical Physics, 142432, Chernogolovka, Russia

    G. M. Tarnopolsky

Authors
  1. M. N. Alfimov
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  2. G. M. Tarnopolsky
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Correspondence to M. N. Alfimov.

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ArXiv ePrint: 1110.5628

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Alfimov, M.N., Tarnopolsky, G.M. Parafermionic Liouville field theory and instantons on ALE spaces. J. High Energ. Phys. 2012, 36 (2012). https://doi.org/10.1007/JHEP02(2012)036

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