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

TL;DR

This paper proves the 5D $A_n$ AGT conjecture at $eta=1$ by introducing a q-deformed $A_n$ Selberg integral and establishing a corresponding average formula involving Schur polynomials.

Contribution

It introduces a generalized q-deformed $A_n$ Selberg integral and proves a new average formula, completing the proof of the 5D $A_n$ AGT conjecture at $eta=1$.

Findings

Proof of the 5D $A_n$ AGT conjecture at $eta=1$

Definition of a q-deformed $A_n$ Selberg integral

Establishment of a q-deformed $A_n$ Selberg average formula

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.