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

G. Arutyunov, S. Penati, A. C. Petkou, A. Santambrogio, E. Sokatchev

TL;DR

The paper analyzes non-protected dimension-four operators in the SU(4) singlet channel of the OPE of two stress-tensor multiplets in ${\cal N}=4$ SYM. By computing the one-loop two-point functions in an ${\cal N}=1$ superspace setup and diagonalizing the resulting anomalous-dimension matrix, the authors identify four quasiprimary operators and find that one has a negative, ${1/N^2}$-suppressed anomalous dimension, interpreted as a binding energy for a two-particle supergravity state. They show that the suppression arises from planar-disconnected contributions that factorize through protected operators, a mechanism that should hold to all orders, and argue that this operator corresponds to a multiparticle state in AdS$_5$ SUGRA, distinct from the K-class that decouples in the gravity limit. The work provides a concrete, perturbative handle on the AdS/CFT dictionary for non-protected, multiparticle states and outlines a general framework for resolving operator mixing and splitting in conformal field theories. In addition, the results are cross-checked against OPE and four-point function analyses, reinforcing the connection between weak-coupling mixing data and strong-coupling AdS/CFT interpretations.

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.

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

TL;DR

The paper analyzes non-protected dimension-four operators in the SU(4) singlet channel of the OPE of two stress-tensor multiplets in SYM. By computing the one-loop two-point functions in an superspace setup and diagonalizing the resulting anomalous-dimension matrix, the authors identify four quasiprimary operators and find that one has a negative, -suppressed anomalous dimension, interpreted as a binding energy for a two-particle supergravity state. They show that the suppression arises from planar-disconnected contributions that factorize through protected operators, a mechanism that should hold to all orders, and argue that this operator corresponds to a multiparticle state in AdS SUGRA, distinct from the K-class that decouples in the gravity limit. The work provides a concrete, perturbative handle on the AdS/CFT dictionary for non-protected, multiparticle states and outlines a general framework for resolving operator mixing and splitting in conformal field theories. In addition, the results are cross-checked against OPE and four-point function analyses, reinforcing the connection between weak-coupling mixing data and strong-coupling AdS/CFT interpretations.

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.

Paper Structure

This paper contains 11 sections, 83 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Non-protected operators in ${\cal N}=4$ SYM
  3. Anomalous dimensions and operator mixing in CFT
  4. Anomalous dimensions of composite operators in CFT
  5. Operator mixing in CFT
  6. Operator splitting in CFT
  7. ${\cal N}=1$ superspace approach
  8. One-loop anomalous dimension matrix and quasiprimary composite operators in ${\cal N}=4$ SYM
  9. Non-protected operators and multi--particle states in supergravity
  10. Four-point functions and the OPE
  11. Diagonalization procedure

Figures (2)

  • Figure 1: Contributions to the tree-level two-point function of ${\cal O}_1$ in the double line notation.
  • Figure 2: Contributions to the one-loop two-point function of ${\cal O}_1$ in the double line notation.