Proof of 5D $A_n$ AGT conjecture at $\beta =1$

Abstract

In this paper, we give a proof of 5D $A_n$ AGT conjecture at $\beta =1$, where the gauge theory side is one dimension higher than the original 4D case, and corresponds to the q-deformation of the 2D conformal field theory side. We define a q-deformed $A_n$ Selberg integral, which generalizes the $A_n$ Selberg integral and the q-deformed $A_1$ Selberg integral in the literature. A q-deformed $A_n$ Selberg average formula with $n+1$ Schur polynomials is proposed and proved to complete the proof.

19 pages; v2: published version, with the conjecture for the q-deformed $A_n$ Selberg average formula of $n+1$ Schur polynomials proved

References in corpus (4)

• Correlation functions in conformal Toda field theory I
• Correlation functions in conformal Toda field theory II
• A direct proof of AGT conjecture at beta = 1
• Quantum toroidal algebras and solvable structures in gauge/string theory