All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry

Abstract

We study correlators of four protected (half-BPS) operators in strongly coupled supersymmetric Yang-Mills theory. These are dual to tree-level supergravity amplitudes on AdS${}_5\times$S${}_5$ for various spherical harmonics on the five-sphere. We use conformal field theory methods, in particular a recently obtained Lorentzian inversion formula, to analytically bootstrap these correlators. The extracted $1/N^2$ double-trace anomalous dimensions confirm a simple pattern recently conjectured by Aprile, Drummond, Heslop and Paul. We explain this pattern by an unexpected ten-dimensional conformal symmetry which appears to be enjoyed by tree-level supergravity (or a suitable subsector of it). The symmetry combines all spherical harmonics into a single ten-dimensional object, and yields compact expressions for the leading logarithmic part of any half-BPS correlator at each loop order.

arXiv comment36+8 pages, 5 figures

References in corpus (54)

• Review of AdS/CFT Integrability: An Overview
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Holography from Conformal Field Theory
• Conformal Partial Waves and the Operator Product Expansion
• Writing CFT correlation functions as AdS scattering amplitudes
• Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N
• The Analytic Bootstrap and AdS Superhorizon Locality
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• Naturalness Versus Supersymmetric Non-renormalization Theorems
• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• A Natural Language for AdS/CFT Correlators
• Light-ray operators in conformal field theory
• Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
• Radial Coordinates for Conformal Blocks
• Large Spin Perturbation Theory
• Unitarity and the Holographic S-Matrix
• Mellin amplitudes for $Ad{S}_5\times S^5$
• Loops in AdS from Conformal Field Theory
• A Mellin space approach to the conformal bootstrap
• A spacetime derivation of the Lorentzian OPE inversion formula
• How to Succeed at Holographic Correlators Without Really Trying
• Conformal Bootstrap in Mellin Space
• Superconformal Ward Identities and their Solution
• Gravitational S-matrix from CFT dispersion relations
• Local bulk S-matrix elements and CFT singularities
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT
• Quantum Gravity from Conformal Field Theory
• Correlation Functions and Massive Kaluza-Klein Modes in the AdS/CFT Correspondence
• Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation
• Unmixing Supergravity
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• The double-trace spectrum of N=4 SYM at strong coupling
• From conformal to Einstein Gravity
• Holographic Reconstruction of AdS Exchanges from Crossing Symmetry
• More $\mathcal{N}=4$ superconformal bootstrap
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• On a Large N Degeneracy in N=4 SYM and the AdS/CFT Correspondence
• Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
• High-energy gravitational scattering and black hole resonances
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Next-next-to-extremal Four Point Functions of N=4 1/2 BPS Operators in the AdS/CFT Correspondence
• Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence
• Four-point functions of different-weight operators in the AdS/CFT correspondence
• Unitarity and positivity constraints for CFT at large central charge
• Four-point functions of 1/2-BPS operators of any weights in the supergravity approximation
• Towards 4-point correlation functions of any 1/2-BPS operators from supergravity
• Revisiting N=4 superconformal blocks
• Covariant propagator in AdS5 x S5 superspace
• Superconformal Invariants or How to Relate Four-point AdS Amplitudes
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering

Cited by in corpus (84)

• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• $20^{\prime }$ Five-Point Function from $Ad{S}_5\times S^5$ Supergravity
• Where is String Theory?
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• Dispersive CFT Sum Rules
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Genus-One String Amplitudes from Conformal Field Theory
• Gluon Scattering in AdS from CFT
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• Bootstrapping the simplest correlator in planar N = 4 SYM at all loops
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• Modular Invariance in Superstring Theory From $\mathcal{N}=4$ Super-Yang-Mills
• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• One-loop amplitudes in $Ad{S}_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling
• CFT Unitarity and the AdS Cutkosky Rules
• Recursion Relations in Witten Diagrams and Conformal Partial Waves
• Ten dimensional symmetry of N=4 SYM correlators
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• All Tree-Level Correlators for M-theory on $Ad{S}_7\times S^4$
• An étude of momentum space scalar amplitudes in AdS
• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
• A Crossing-Symmetric OPE Inversion Formula
• Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator
• Holographic correlators in AdS${}_3$ without Witten diagrams
• Holographic correlators in AdS${}_3$
• Loops in AdS: From the Spectral Representation to Position Space
• Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM
• Growing Extra Dimensions in AdS/CFT
• The CFT${}_6$ origin of all tree-level 4-point correlators in AdS${}_3\times S^3$
• String corrections to AdS amplitudes and the double-trace spectrum of N=4 SYM
• One-loop Gluon Amplitudes in AdS
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Towards the Virasoro-Shapiro Amplitude in AdS5xS5
• On spinning loop amplitudes in Anti-de Sitter space
• All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs
• Maximal $U(1{)}_Y$-violating $n$-point correlators in $\mathcal{N}=4$ super-Yang-Mills theory
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• The Virasoro-Shapiro amplitude in AdS${}_5\times$S${}^5$ and level splitting of 10d conformal symmetry
• Dispersion Relation for CFT Four-Point Functions
• Helicity basis for three-dimensional conformal field theory
• Modular invariant holographic correlators for $\mathcal{N}=4$ SYM with general gauge group
• One-loop string corrections to AdS amplitudes from CFT
• 6d (2,0) and M-theory at 1-loop
• Graviton scattering in self-dual radiative space-times
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Coupled minimal models revisited
• Heavy-light Bootstrap from Lorentzian Inversion Formula
• All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT
• Opacity from Loops in AdS
• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• Loops in AdS: From the Spectral Representation to Position Space II
• Towards All Loop Supergravity Amplitudes on $Ad{S}_5\times S^5$
• AdS super gluon scattering up to two loops: A position space approach
• More on holographic correlators: Twisted and dimensionally reduced structures
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• One-loop string corrections for AdS Kaluza-Klein amplitudes
• Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian
• Spinning correlators in $\mathcal{N}=2$ SCFTs: Superspace and AdS amplitudes
• Higher-Dimensional Symmetry of AdS${}_2\times$S${}^2$ Correlators
• Regge trajectories for the (2,0) theories
• Recursion Relations for Anomalous Dimensions in the 6d $(2,0)$ Theory
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• On the spectrum and structure constants of short operators in N=4 SYM at strong coupling
• Notes on gravity multiplet correlators in $Ad{S}_3\times S^3$
• Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
• Mixed Correlator Dispersive CFT Sum Rules
• The Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space
• Three-point functions at strong coupling in the BMN limit
• $Ad{S}_5\times S^5$ supergravity vertex operators
• One-loop string amplitudes in AdS${}_5\times$S${}^5$: Mellin space and sphere splitting
• Bootstrapping string theory on AdS${}_5\times S^5$
• All Next-to-Next-to-Extremal One-Loop Correlators of AdS Supergluons and Supergravitons
• More on Heavy-Light Bootstrap up to Double-Stress-Tensor
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Four-point correlators in N=4 SYM from AdS${}_5$ bubbling geometries
• Non-analytic terms of string amplitudes from partial waves
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Conformal bootstrap in momentum space at finite volume
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM