R-Current Correlators in N=4 Super Yang-Mills Theory from Anti-de Sitter Supergravity

TL;DR

This paper verifies the AdS/CFT correspondence by comparing two- and three-point functions of R-symmetry currents in N=4 super Yang-Mills theory and IIB supergravity, confirming the relationship at one-loop level.

Contribution

It demonstrates the matching of two- and three-point correlators between super Yang-Mills theory and supergravity, revealing the structure of three-point functions without complex loop calculations.

Findings

Two- and three-point functions match at one-loop in N=4 SYM.

Supergravity correlators resemble one-loop triangle diagrams.

Higher-point functions can be analyzed similarly.

Abstract

We test the conjectured relationship between N=4 super Yang-Mills theory in four dimensions and IIB supergravity compactified on $AdS_5\times S_5$ by computing the two- and three-point functions of R-symmetry currents. We observe that the integral expressions describing the general three-point correlator on the supergravity side have a structure similar to one-loop triangle diagrams in N=4 super Yang-Mills theory. This allows us to compare the expressions on both sides of the AdS/CFT correspondence without the technical complications of the loop integrations. We confirm that the two- and three-point correspondence arises at only one-loop in the N=4 super Yang-Mills theory. Higher-point functions as well as further three-point functions may be analyzed similarly.