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.

arXiv comment19 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 (20)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• Correlation functions in conformal Toda field theory I
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Correlation functions in conformal Toda field theory II
• Proving AGT conjecture as HS duality: extension to five dimensions
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• Five-dimensional AGT Relation and the Deformed beta-ensemble
• A direct proof of AGT conjecture at beta = 1
• Yangian realisations from finite W algebras
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• A slow review of the AGT correspondence
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• Selberg Integral and SU(N) AGT Conjecture
• A Selberg integral for the Lie algebra A_n
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
• AFLT-type Selberg integrals