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The matrix model version of AGT conjecture and CIV-DV prepotential

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Abstract

Recently exact formulas were provided for partition function of conformal (multi-Penner) β-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted as Dotsenko-Fateev correlator of screenings and analytically continued in the number of screening insertions, represents generic Virasoro conformal blocks. Actually these formulas describe the lowest terms of the q a -expansion, where q a parameterize the shape of the Penner potential, and are exact in the filling numbers N a . At the same time, the older theory of CIV-DV prepotential, straightforwardly extended to arbitrary β and to non-polynomial potentials, provides an alternative expansion: in powers of N a and exact in q a . We check that the two expansions coincide in the overlapping region, i.e. for the lowest terms of expansions in both q a and N a . This coincidence is somewhat non-trivial, since the two methods use different integration contours: integrals in one case are of the B-function (Euler-Selberg) type, while in the other case they are Gaussian integrals.

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  1. Theory Department, Institute for Theoretical and Experimental Physics (ITEP), Bolshaya Cheremushkinskaya, Moscow, Russia

    A. Morozov & Sh. Shakirov

  2. Department of General and Applied Physics, Moscow Institute of Physics and Technology, Institutskii per., Dolgoprudny, Russia

    Sh. Shakirov

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Morozov, A., Shakirov, S. The matrix model version of AGT conjecture and CIV-DV prepotential. J. High Energ. Phys. 2010, 66 (2010). https://doi.org/10.1007/JHEP08(2010)066

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