Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
Mar, 201039 pages
Published in:
- Nucl.Phys.B 838 (2010) 298-330
e-Print:
- 1003.2929 [hep-th]
Report number:
- OCU-PHYS-327
View in:
Citations per year
Abstract: (Elsevier)
We observe that, at β -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 N f = 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.Note:
- 39 pages, 1 figure; v2: typos and minor errrors in Eqs. (6.39) and (6.41) corrected, to appear in Nucl. Phys. B
- matrix model
- conformal
- deformation
- Penner model
- free energy
- partition function
- perturbation theory: higher-order
- loop space
- expansion 1/N
- bibliography
References(86)
Figures(1)