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Abstract: The recent AGT suggestion to use the set of Nekrasov functions as a basis fora linear decomposition of generic conformal blocks works very well not only inthe case of Virasoro symmetry, but also for conformal theories with extendedchiral algebra. This is rather natural, because Nekrasov functions areintroduced as expansion basis for generalized hypergeometric integrals, verysimilar to those which arise in expansion of Dotsenko-Fateev integrals inpowers of alpha-parameters. Thus, the AGT conjecture is closely related to theold belief that conformal theory can be effectively described in the free fieldformalism, and it can actually be a key to clear formulating and proof thislong-standing hypothesis. As an application of this kind of reasoning we useknowledge of the exact hypergeometric conformal block for complete proof of theAGT relation for a restricted class of external states.

Autor: A.Mironov, A.Morozov


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