Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals

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Abstract

The AGT relation identifies the Nekrasov functions for various N = 2 SUSY gauge theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev matrix model (β-ensemble) representations the latter being polylinear combinations of Selberg integrals. The "pure gauge" limit of these matrix models is, however, a non-trivial multiscaling large-N limit, which requires a separate investigation. We show that in this pure gauge limit the Selberg integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the Nekrasov function for pure SU(2) theory acquires a form very much reminiscent of the AMM decomposition formula for some model X into a pair of the BGW models. At the same time, X, which still has to be found, is the pure gauge limit of the elliptic Selberg integral. Presumably, it is again a BGW model, only in the Dijkgraaf-Vafa double cut phase. © SISSA 2011.

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Mironov, A., Morozov, A., & Shakirov, S. (2011). Brezin-Gross-Witten model as “pure gauge” limit of Selberg integrals. Journal of High Energy Physics, 2011(3). https://doi.org/10.1007/JHEP03(2011)102

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