Non-protected operators in N=4 SYM and multiparticle states of AdS_5 SUGRA

TL;DR

This paper investigates non-protected operators in N=4 SYM, revealing a suppressed anomalous dimension operator that likely corresponds to a multiparticle supergravity state in AdS/CFT.

Contribution

It identifies and diagonalizes the mixing of quadrilinear scalar operators, discovering a unique operator with suppressed anomalous dimension, suggesting a multiparticle state dual in AdS/CFT.

Findings

Found an operator with negative, suppressed anomalous dimension.

Resolved operator mixing via one-loop two-point functions.

Proposed duality to a multiparticle supergravity state.

Abstract

We study a class of non-protected local composite operators which occur in the R symmetry singlet channel of the OPE of two stress-tensor multiplets in {\cal N}=4 SYM. At tree level these are quadrilinear scalar dimension four operators, two single-traces and two double-traces. In the presence of interaction, due to a non-trivial mixing under renormalization, they split into linear combinations of conformally covariant operators. We resolve the mixing by computing the one-loop two-point functions of all the operators in an {\cal N}=1 setup, then diagonalizing the anomalous dimension matrix and identifying the quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by a factor of 1/N^2 with respect to the anomalous dimensions of the Konishi-like operators. We reveal the mechanism responsible for this suppression and argue that it works at every order in perturbation theory. In the context of the AdS/CFT correspondence such an operator should be dual to a multiparticle supergravity state whose energy is less than the sum of the corresponding individual single-particle states.