On the relations between correlation functions in SYM/pp–wave correspondence

In this note we establish the explicit relation between correlation functions in N = 4 SUSY Yang–Mills theory on S3×R in a double scaling limit and scattering amplitudes of the String Theory on the pp-wave background. The relation is found for two– and three– point correlation functions in these theories. As a by product we formulate a dictionary for the correspondence between these theories: in particular, we find some unknown relations between the parameters in these theories. Furthermore, we argue that the String Theory on the pp–wave background is related to four–dimensional SUSY Yang–Mills theory rather than to the reduced matrix quantum mechanics. We identify string theory excitations which are related to the Kaluza–Klein excitation of the Yang–Mills theory on S3.