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

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.

Latex, 32 pages, 5 figures

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Cited by in corpus (44)

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• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Effective Conformal Theory and the Flat-Space Limit of AdS
• On stringy AdS_5 x S^5 and higher spin holography
• Higher Spin Symmetry and N=4 SYM
• Conformal Partial Wave Expansions for N=4 Chiral Four Point Functions
• Three-Point Functions in N=4 SYM Theory at One-Loop
• On the spectrum of AdS/CFT beyond supergravity
• More $\mathcal{N}=4$ superconformal bootstrap
• BMN Operators and Superconformal Symmetry
• Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
• The 3-string vertex and the AdS/CFT duality in the PP-wave limit
• BMN Operators for N=1 Superconformal Yang-Mills Theories and Associated String Backgrounds
• Four-point correlators of BPS operators in N=4 SYM at order g^4
• Multitrace deformations, Gamow states, and Stability of AdS/CFT
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Permutations and the Loop
• Spin bit models from non-planar N=4 SYM
• On the perturbative chiral ring for marginally deformed N=4 SYM theories
• Surprises from the Resolution of Operator Mixing in N = 4 SYM
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• BPS Chaos
• Quarter BPS classified by Brauer algebra
• The Duality between IIB String Theory on PP-wave and N=4 SYM: a Status Report
• On instanton contributions to anomalous dimensions in N=4 supersymmetric Yang-Mills theory
• String amplitudes in the Hpp-wave limit of AdS3xS3
• On two fermion BMN operators
• Modular interpolating functions for N=4 SYM
• Positive Energy Unitary Irreducible Representations of the Superalgebras osp(1|2n,R)
• Operator Mixing and the AdS/CFT correspondence
• Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry
• Negative anomalous dimensions in N=4 SYM
• One-loop string amplitudes in AdS${}_5\times$S${}^5$: Mellin space and sphere splitting
• Anomalous Dimensions from Thermal AdS Partition Functions
• On instanton effects in the operator product expansion
• S-duality invariant perturbation theory improved by holography
• Non-planar operator mixing by Brauer representations
• Rationality of the Anomalous Dimensions in N=4 SYM theory
• Two-point functions for N=4 Konishi-like operators
• On interpolating anomalous dimension of twist-two operators with general spins