Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-11-30
JHEP 1002:030,2010
Physics
High Energy Physics
High Energy Physics - Theory
14 pages
Scientific paper
10.1007/JHEP02(2010)030
We give a concise summary of the impressive recent development unifying a number of different fundamental subjects. The quiver Nekrasov functions (generalized hypergeometric series) form a full basis for all conformal blocks of the Virasoro algebra and are sufficient to provide the same for some (special) conformal blocks of W-algebras. They can be described in terms of Seiberg-Witten theory, with the SW differential given by the 1-point resolvent in the DV phase of the quiver (discrete or conformal) matrix model (\beta-ensemble), dS = ydz + O(\epsilon^2) = \sum_p \epsilon^{2p} \rho_\beta^{(p|1)}(z), where \epsilon and \beta are related to the LNS parameters \epsilon_1 and \epsilon_2. This provides explicit formulas for conformal blocks in terms of analytically continued contour integrals and resolves the old puzzle of the free-field description of generic conformal blocks through the Dotsenko-Fateev integrals. Most important, this completes the GKMMM description of SW theory in terms of integrability theory with the help of exact BS integrals, and provides an extended manifestation of the basic principle which states that the effective actions are the tau-functions of integrable hierarchies.
Mironov Aleksej
Morozov Alexander
Shakirov Sh.
No associations
LandOfFree
Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-444185