Holographic Normal Ordering and Multi-particle States in the AdS/CFT Correspondence

TL;DR

This paper introduces a novel renormalization method for correlators in N=4 supersymmetric gauge theory within the AdS/CFT framework, addressing divergences and their relation to multi-particle states.

Contribution

It proposes a boundary theory-based renormalization approach that differs from standard normal ordering, linking contact terms to multi-particle states in the dual gravity description.

Findings

Renormalization via boundary theory effectively handles divergences.

Contact terms are related to multi-particle correlation functions.

The approach clarifies the structure of correlators in AdS/CFT.

Abstract

The general correlator of composite operators of N=4 supersymmetric gauge field theory is divergent. We introduce a means for renormalizing these correlators by adding a boundary theory on the AdS space correcting for the divergences. Such renormalizations are not equivalent to the standard normal ordering of current algebras in two dimensions. The correlators contain contact terms that contribute to the OPE; we relate them diagrammatically to correlation functions of compound composite operators dual to multi-particle states.