Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling

Abstract

We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators $O^{I} \sim \tr ϕ^{(i}ϕ^{j)}$ in $\mathbb{N}=4$ SYM${}_4$ at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R-symmetry current and the stress tensor. Operators dual to string modes decouple at strong coupling. We compute the anomalous dimensions and the leading $1/N^2$ corrections to the normalization constants of the 2- and 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5 respectively. We also find that the conformal dimensions of certain towers of double-trace operators in the {\bf 105}, {\bf 84} and {\bf 175} irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the {\bf 20} irrep, its anomalous dimension vanishes. As by-products of our investigation, we derive explicit expressions for the conformal block of the stress tensor, and for the conformal partial wave amplitudes of a conserved current and of a stress tensor in $d$ dimensions.

Latex, 47p, subsection 4.5 is modified, typos are corrected

References in corpus (7)

• Three-Loop Four-Point Correlator in N=4 SYM
• The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
• Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation
• Scalar Quartic Couplings in Type IIB Supergravity on $Ad{S}_5\times S^5$
• Superconformal Field Theories, Multiplet Shortening, and the AdS${}_5$/SCFT${}_4$ Correspondence
• A note on the analyticity of AdS scalar exchange graphs in the crossed channel
• A note on R-currents and trace anomalies in the (2,0) tensor multiplet in d=6 and AdS/CFT correspondence

Cited by in corpus (121)

• AdS Dual of the Critical O(N) Vector Model
• An Index for 4 dimensional Super Conformal Theories
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Conformal Four Point Functions and the Operator Product Expansion
• Magic identities for conformal four-point integrals
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• The N=4 Superconformal Bootstrap
• Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• Effective Conformal Theory and the Flat-Space Limit of AdS
• Precision Spectroscopy of AdS/CFT
• Superconformal Ward Identities and their Solution
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT
• Notes On Higher Spin Symmetries
• From Free Fields to $AdS$
• From correlation functions to event shapes
• Rigorous Limits on the Interaction Strength in Quantum Field Theory
• Correlation Functions and Massive Kaluza-Klein Modes in the AdS/CFT Correspondence
• $20^{\prime }$ Five-Point Function from $Ad{S}_5\times S^5$ Supergravity
• Event shapes in N=4 super-Yang-Mills theory
• Higher-spin correlators
• Unmixing Supergravity
• From Free Fields to $AdS$ -- III
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• A three-loop test of the dilatation operator in N=4 SYM
• Conformal Partial Wave Expansions for N=4 Chiral Four Point Functions
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• Spinning Witten Diagrams
• Deep inelastic scattering off a N=4 SYM plasma at strong coupling
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• Exceptional non-renormalization properties and OPE analysis of chiral four-point functions in N=4 SYM_4
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• Holographic Reconstruction of AdS Exchanges from Crossing Symmetry
• More $\mathcal{N}=4$ superconformal bootstrap
• BMN Operators and Superconformal Symmetry
• Four-point correlation function of stress-energy tensors in N=4 superconformal theories
• On Non-renormalization and OPE in Superconformal Field Theories
• Holomorphic Factorization for a Quantum Tetrahedron
• OPEs and 3-point correlators of protected operators in N=4 SYM
• On the OPE of 1/2 BPS Short Operators in N=4 SCFT${}_4$
• N=4 Superconformal Characters and Partition Functions
• On a Large N Degeneracy in N=4 SYM and the AdS/CFT Correspondence
• On Operator Mixing in N=4 SYM
• Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
• Perturbative and instanton corrections to the OPE of CPOs in N=4 SYM_4
• A note on composite operators in N=4 SYM
• SUSY Splits, But Then Returns
• Quantum ${\varphi }^4$ Theory in AdS${}_4$ and its CFT Dual
• Non-protected operators in N=4 SYM and multiparticle states of AdS_5 SUGRA
• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD
• Generalized bootstrap equations for N=4 SCFT
• Four-point functions in N=4 SYM
• Instanton corrections to circular Wilson loops in N=4 Supersymmetric Yang-Mills
• Implications of Superconformal Symmetry for Interacting (2,0) Tensor Multiplets
• Next-next-to-extremal Four Point Functions of N=4 1/2 BPS Operators in the AdS/CFT Correspondence
• Systematics of Quarter BPS operators in N=4 SYM
• Holographic 4-point correlators with heavy states
• Cubic couplings in D=6 N=4b supergravity on AdS_3\times S^3
• Subleading Eikonal, AdS/CFT and Double Stress Tensors
• Three-Point Functions of Quarter BPS Operators in N=4 SYM
• Aspects of N=4 SYM
• Four-point correlators of BPS operators in N=4 SYM at order g^4
• Universal properties of superconformal OPEs for 1/2 BPS operators in $3\le D\le 6$
• Duality between Wilson loops and gluon amplitudes
• Orbiting strings in AdS black holes and N=4 SYM at finite temperature
• Three-loop universal structure constants in N=4 susy Yang-Mills theory
• Four-point functions of different-weight operators in the AdS/CFT correspondence
• Aspects of superconformal field theories in six dimensions
• Surprises from the Resolution of Operator Mixing in N = 4 SYM
• Integral invariants in maximally supersymmetric Yang-Mills theories
• The role of leading twist operators in the Regge and Lorentzian OPE limits
• Superconformal partial waves in Grassmannian field theories
• On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
• On instanton contributions to anomalous dimensions in N=4 supersymmetric Yang-Mills theory
• Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory
• Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions
• String amplitudes in the Hpp-wave limit of AdS3xS3
• Operator mixing and three-point functions in N=4 SYM
• Partial wave expansion and Wightman positivity in conformal field theory
• On two fermion BMN operators
• Holography, Duality and Higher-Spin Theories
• Superconformal Invariants or How to Relate Four-point AdS Amplitudes
• (Non-)perturbative tests of the AdS/CFT correspondence
• Boundary multi-trace deformations and OPEs in AdS/CFT correspondence
• Some Systematics of the Coupling Constant Dependence of N=4 Yang-Mills
• Flavour singlets in gauge theory as Permutations
• BPS saturation of the N=4 monopole by infinite composite-operator renormalization
• Unparticle self-interactions
• Lessons from crossing symmetry at large N
• AdS/SCFT in Superspace
• AdS/CFT for Four-Point Amplitudes involving Gravitino Exchange
• Matching three-point functions of BMN operators at weak and strong coupling
• Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
• On twist-two operators in N=4 SYM
• A Curious Truncation of N=4 Yang-Mills
• Gauge-invariant correlation functions in light-cone superspace
• SO_0(1,d+1) Racah coefficients: Type I representations
• Negative anomalous dimensions in N=4 SYM
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Multi-trace quasi-primary fields of $\mathcal{N}=4$ $SY{M}_4$ from AdS n-point functions
• Exact holographic RG flows in extended SUGRA
• AdS Box Graphs, Unitarity and Operator Product Expansions
• Instanton effects in correlation functions on the light-cone
• Knitting Wormholes by Entanglement in Supergravity
• Anomalous Dimensions from Thermal AdS Partition Functions
• Circular Wilson loops in defect $\mathcal{N}$=4 SYM: phase transitions, double-scaling limits and OPE expansion
• Twistors, CFT and Holography
• S-duality invariant perturbation theory improved by holography
• Stress Tensor Sector of Conformal Correlators
• Fractional Multi-Trace Fields of N=4 SYM_4 from AdS/CFT
• Rationality of the Anomalous Dimensions in N=4 SYM theory
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Holography for the Lorentz Group Racah Coefficients
• Superconformal Symmetry and Correlation Functions
• On interpolating anomalous dimension of twist-two operators with general spins