Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions

TL;DR

This paper explores five-dimensional AGT correspondence using q-deformed beta-ensembles, introducing generalized Macdonald polynomials, establishing spectral duality, and connecting topological strings with q-Liouville theory.

Contribution

It introduces a special basis of states with generalized Macdonald polynomials and proves spectral duality for Nekrasov functions in five dimensions.

Findings

Derived loop equations for the beta-ensemble

Proved spectral duality for Nekrasov functions

Clarified relation between topological strings and q-Liouville

Abstract

We study five dimensional AGT correspondence by means of the q-deformed beta-ensemble technique. We provide a special basis of states in the q-deformed CFT Hilbert space consisting of generalized Macdonald polynomials, derive the loop equations for the beta-ensemble and obtain the factorization formulas for the corresponding matrix elements. We prove the spectral duality for Nekrasov functions and discuss its meaning for conformal blocks. We also clarify the relation between topological strings and q-Liouville vertex operators.