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Proving AGT conjecture as HS duality: extension to five dimensions · Around

2011

Proving AGT conjecture as HS duality: extension to five dimensions

Mironov, A., Morozov, A., Shakirov, Sh. et al.

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We extend the proof from arXiv:1012.3137, which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories.

This involves an additional q-deformation.
Not surprisingly, the extension turns out to be trivial: it is enough to substitute all relevant numbers by q-numbers in all the formulas, Dotsenko-Fateev integrals by the Jackson sums and the Jack polynomials by the MacDonald ones.
The problem with extra poles in individual Nekrasov functions continues to exist, therefore, such a proof works only for \beta = 1, i.e.

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Andrey Mironov, Sergey Mironov, Alexei Morozov and Andrey Morozov, Theor.Math.Phys. 165 (2010) 1662-1698 (Teor.Mat.Fiz. 165 (2010) 503-542), arXiv:0908.2064

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