Near-extremal correlators and vanishing supergravity couplings in AdS/CFT

TL;DR

This paper investigates near-extremal correlators in AdS/CFT, showing their structure matches non-renormalized field theory results and proposing vanishing of certain supergravity couplings for full consistency.

Contribution

It demonstrates the factorization of near-extremal correlators and conjectures the vanishing of specific supergravity couplings to align with field theory.

Findings

Correlators factor into lower-point functions at order g^2.

Supergravity exchange diagrams match the factored structure.

Contact diagrams would disrupt the structure, implying their couplings vanish.

Abstract

We study near-extremal n-point correlation functions of chiral primary operators, in which the maximal scale dimension k is related to the others by k=\sum_i k_i-m with m equal to or smaller than n-3. Through order g^2 in field theory, we show that these correlators are simple sums of terms each of which factors into products of lower-point correlators. Terms which contain only factors of two- and three-point functions are not renormalized, but other terms have non-vanishing order g^2 corrections. We then show that the contributing AdS exchange diagrams neatly match this factored structure. In particular, for n=4,5 precise agreement in form and coefficient is established between supergravity and the non-renormalized factored terms from field theory. On the other hand, contact diagrams in supergravity would produce a non-factored structure. This leads us to conjecture that the corresponding bulk couplings vanish, so as to achieve full agreement between the structure of these correlators in supergravity and weak-coupling field theory.