Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver

TL;DR

This paper provides evidence for the AGT-W relation connecting SU(3) quiver gauge theories with A_2 Toda theory by deriving explicit correlation functions and confirming their agreement with Nekrasov's partition function.

Contribution

It introduces an algorithm to compute n-point correlation functions in A_2 Toda theory and applies it to verify the AGT-W relation for specific quivers.

Findings

Explicit 5-point correlation functions match Nekrasov's partition function.

Algorithm applicable to general n-point functions in A_2 Toda theory.

Partial analysis suggests potential for broader quiver relations.

Abstract

We give some evidences of the AGT-W relation between SU(3) quiver gauge theories and A_2 Toda theory. In particular, we derive the explicit form of 5-point correlation functions in the lower orders and confirm the agreement with Nekrasov's partition function for SU(3)xSU(3) quiver gauge theory. The algorithm to derive the correlation functions can be applied to general n-point function in A_2 Toda theory which will be useful to establish the relation for more generic quivers. Partial analysis is also given for SU(3)xSU(2) case and we comment on some technical issues which need clarification before establishing the relation.