Multi-trace quasi-primary fields of $\mathcal{N}=4$ $SYM_4$ from AdS n-point functions

TL;DR

This paper introduces a recursive algorithm to analyze infinite sequences of quasi-primary fields in $ ext{AdS}_5/ ext{CFT}_4$ correspondence, revealing BPS fields with vanishing anomalous dimensions through conformal partial wave analysis.

Contribution

It develops a novel recursive method to study quasi-primary fields from chiral primary operators and derives $rac{1}{N^2}$ corrections to 4-point functions in AdS/CFT.

Findings

Identifies infinite sequences of quasi-primary fields with zero anomalous dimensions.

Expresses normal products of $O_2$ operators using SO(20) projection operators.

Derives $rac{1}{N^2}$ corrections to 4-point functions.

Abstract

We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fields obtained from chiral primary operators (CPOs) $O^I_k(x)$ and eventually their derivatives by applying operator product expansions and singling out SO(6) representations. We show that normal products of $O_2$ operators can be expressed in terms of projection operators on representations of SO(20) and discuss intertwining operators for SO(6) representations. Furthermore we derive $\mathcal{O}(\frac{1}{N^2})$ corrections to AdS/CFT 4-point functions by graphical combinatorics and finally extract anomalous dimensions by applying the method of conformal partial wave analysis. We find infinite sequences of quasi-primary fields with vanishing anomalous dimensions and interpret them as 1/2-BPS or 1/4-BPS fields.