Analysis of correlation functions in Toda theory and the Alday-Gaiotto-Tachikawa-Wyllard relation for SU(3) quiver

We give some evidences of the Alday-Gaiotto-Tachikawa-Wyllard 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) x SU(3) quiver gauge theory. The algorithm to derive the correlation functions can be applied to a general n-point function in A2 Toda theory, which will be useful to establish the relation for more generic quivers. Partial analysis is also given for the SU(3) x SU(2) case, and we comment on some technical issues that need clarification before establishing the relation.