2010/03/31 by Hiroshi Itoyama, Takeshi Oota · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2010.05.002
published as Nucl.Phys.B838:298-330,2010 · 39 pages, 1 figure; v2: typos and minor errrors in Eqs. (6.39) and (6.41) corrected, to appear in Nucl. Phys. B
arxiv created 2010/05/23 · arxiv updated 2014/11/20
We observe that, at beta-deformed matrix models for the four-point conformal block, the point q=0 is the point where the three-Penner type model becomes a pair of decoupled two-Penner type models and where, in the planar limit, (an array of) two-cut eigenvalue distribution(s) coalesce into (that of) one-cut one(s). We treat the Dotsenko-Fateev multiple integral, with their paths under the recent discussion, as perturbed double-Selberg matrix model (at q=0, it becomes a pair of Selberg integrals) to construct two kinds of generating functions for the q-expansion coefficients and compute some. A formula associated with the Jack polynomial is noted. The second Nekrasov coefficient for SU(2) with Nf =4 is derived. A pair of Young diagrams appears naturally. The finite N loop equation at q=0 as well as its planar limit is solved exactly, providing a useful tool to evaluate the coefficients as those of the resolvents. The planar free energy in the q-expansion is computed to the lowest non-trivial order. A free field representation of the Nekrasov function is given.