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Article

Parafermionic Liuoville field theory and instantons on ALE spaces

Journal of High Energy Physics. 2012. No. 02. P. 36-56.
M.N. Alfimov, Tarnopolsky G.

In this paper we study the correspondence between the $\widehat{\mathfrak{su}}(n)_k \oplus \widehat{\mathfrak{su}}(n)_p/\widehat{\mathfrak{su}}(n)_{k+p}$ coset conformal field theories and N=2 SU(n) gauge theories on R^4/Z_p. Namely we check the correspondence between the SU(2) Nekrasov partition function on R^4/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 R^4/Z_p we also find some evidence that this correspondence with arbitrary p takes place up to the U(1)-factor.