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

TL;DR

This paper establishes a direct relation between correlation functions in ${ m extbf{N=4}}$ SUSY Yang--Mills theory on $S^3 imes R$ and string scattering amplitudes on the pp-wave background, revealing new insights into their correspondence.

Contribution

It explicitly relates two- and three-point correlation functions in SYM theory to string scattering amplitudes and formulates a detailed dictionary for their correspondence, including parameter relations.

Findings

Derived explicit relations between SYM correlators and string amplitudes.

Formulated a dictionary linking parameters of the two theories.

Identified string excitations corresponding to Yang--Mills Kaluza--Klein modes.

Abstract

In this note we establish the explicit relation between correlation functions in ${\cal N} = 4$ SUSY Yang--Mills theory on $S^3\times R$ 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 $S^3$.