Towards a proof of the AGT conjecture
Alexei Morozov
The AGT conjecture identifies the conformal blocks
of 2d CFT with Nekrasov's expansion of
prepotentials in N=2 SYM theories in 4d.
In the free-field formalism conformal blocks
can be represented in terms of Dotsenko-Fateev
integrals and acquire the form of
the correlators in Penner beta-ensemble --
a special kind of an eigenvalue matrix model.
From this perspective the two sides of the
AGT conjecture look like the two kinds of bilinear
expansions of a particular correlator,
which can be explicitly evaluated with the help
of Selberg integrals.