Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver

TL;DR

This paper investigates the 3-point functions in A_{N-1} Toda theory and confirms the AGT-W relation by matching these functions with the 1-loop partition functions of 4D N=2 SU(N) quiver gauge theories.

Contribution

It provides a detailed analysis of 3-point functions in Toda theory and verifies the AGT-W relation for all SU(N) quiver gauge groups.

Findings

Successful verification of the 1-loop AGT-W relation for all SU(N) quivers.

Demonstrates the correspondence between Toda 3-point functions and gauge theory partition functions.

Extends previous results to a general class of SU(N) quiver gauge theories.

Abstract

We study on the property of 3-point correlation functions of 2-dim A_{N-1} Toda field theory, and show the correspondence with the 1-loop part of partition function of 4-dim N=2 SU(N) quiver gauge theory. As a result, we can check successfully the 1-loop part of AGT-W relation for all the cases of SU(N) quiver gauge group.