A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories

TL;DR

This paper establishes a new correspondence between 2D A_{N-1} conformal Toda theory correlation functions and 4D N=2 SU(N) quiver gauge theory instanton partition functions, extending known Liouville theory relations.

Contribution

It generalizes the AGT correspondence from Liouville to Toda theories, revealing new features specific to higher-rank gauge groups.

Findings

Derived explicit relations between Toda correlators and Nekrasov functions.

Identified novel features absent in Liouville case.

Extended the AGT correspondence to a broader class of theories.

Abstract

We propose a relation between correlation functions in the 2d A_{N-1} conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N=2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently uncovered relation between the Liouville theory and SU(2) quivers. New features appear in the analysis that have no counterparts in the Liouville case.