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

TL;DR

This paper tests the AdS/CFT correspondence by comparing ${SU(4)}$ R-current correlators in ${ m N}=4$ SYM with their counterparts computed from IIB supergravity on ${ m AdS}_5\times S^5$. The authors derive AdS results using the boundary-to-bulk kernel and analyze momentum-space correlators, revealing a triangle-structure in the bulk integrals that mirrors one-loop YM diagrams, enabling direct integrand-level comparison. They perform a one-loop calculation in ${ m N}=4$ SYM and show exact agreement with the AdS results after fixing normalization constants, providing evidence for a non-renormalization of the vector part and the Adler-Bardeen-like behavior of the anomalous part. The method avoids full loop integrations and offers a practical route to higher-point AdS/CFT tests by matching integrands between gravity and gauge theory.

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.