Field Theory Tests for Correlators in the AdS/CFT Correspondence

TL;DR

This paper calculates radiative corrections to certain correlators in N=4 supersymmetric Yang-Mills theory, finding they vanish at order g^2, supporting superconformal nonrenormalization theorems and AdS/CFT correspondence predictions.

Contribution

It provides explicit g^2 corrections to 2- and 3-point correlators, confirming their vanishing and supporting theoretical conjectures in the AdS/CFT framework.

Findings

All computed 2- and 3-point correlators have vanishing g^2 corrections.

Supports superconformal nonrenormalization theorems.

Confirms predictions from supergravity calculations at large N.

Abstract

The order g^2 radiative corrections to all 2- and 3-point correlators of the composite primary operators Tr X^k are computed in {\cal N} = 4 supersymmetric Yang-Mills theory with gauge group SU(N). Corrections are found to vanish for all N. For k=2 this is a consequence of known superconformal nonrenormalization theorems, and for general k the result confirms an N-to-infinity, fixed large g^2N supergravity calculation and further conjectures in hep-th/9806074. A 3-point correlator involving {\cal N} = 4 descendents of Tr X^2 is calculated, and its order g^2 contribution also vanishes, giving evidence for the absence of radiative corrections in correlators of descendent operators.