Finalizing the proof of AGT relations with the help of the generalized Jack polynomials

Understand

Original proofs of the AGT relations with the help of the Hubbard-Stratanovich duality of the modified Dotsenko-Fateev matrix model did not work for beta different from one, because Nekrasov functions were not properly reproduced by Selberg-Kadell integrals of Jack polynomials.

• We demonstrate that if the generalized Jack polynomials, depending on the N-ples of Young diagrams from the very beginning, are used instead of the N-linear combinations of ordinary Jacks, this resolves the problem.
• Such polynomials naturally arise as special elements in the equivariant cohomologies of the GL(N)-instanton moduli spaces, and this also establishes connection to alternative ABBFLT approach to the AGT relations, studying the action of chiral algebras on the instanton moduli spaces.
• In this paper we describe a complete proof of AGT in the simple case of GL(2) (N=2) Yang-Mills theory, i.e.