Proving AGT conjecture as HS duality: Extension to five dimensions

DOI10.1016/J.NUCLPHYSB.2011.09.021zbMATH Open1229.81184arXiv1105.0948OpenAlexW2012726609WikidataQ123197319 ScholiaQ123197319MaRDI QIDQ659412

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Publication date: 18 January 2012

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Abstract: 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 �eta = 1, i.e. for q=t in MacDonald's notation. For �eta e 1 the conformal blocks are related in this way to a non-Nekrasov decomposition of the LMNS partition function into a double sum over Young diagrams.

Full work available at URL: https://arxiv.org/abs/1105.0948

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