All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT

Abstract

We computed a set of structures which appear in the four-point function of protected operators of dimension two in $\mathcal{N}=4$ Super Yang Mills with $SU(N)$ gauge group, at any order in a large $N$ expansion. They are determined only by leading order CFT data. By focusing on a specific limit, we made connection with the dual supergravity amplitude in flat space, where such structures correspond to iterated $s$-cuts. We made several checks and we conjecture that the same interpretation holds for supergravity amplitudes on $Ad{S}_5\times S^5$.

arXiv comment43 pages, Ancillary files contains various results presented in the paper. V2: Corrected typos, added references and modified figure. V3: reformatted for J.Phys. A, accepted version

References in corpus (66)

• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• Holography from Conformal Field Theory
• Differential Equations for Feynman Graph Amplitudes
• Dimensionally Regulated Pentagon Integrals
• Writing CFT correlation functions as AdS scattering amplitudes
• Analyticity in Spin in Conformal Theories
• Connection between Feynman integrals having different values of the space-time dimension
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• HPL, a Mathematica implementation of the harmonic polylogarithms
• A Natural Language for AdS/CFT Correlators
• Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
• A Systematic and Efficient Method to Compute Multi-loop Master Integrals
• Mellin amplitudes for $Ad{S}_5\times S^5$
• Reducing differential equations for multiloop master integrals
• Loops in AdS from Conformal Field Theory
• Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• How to Succeed at Holographic Correlators Without Really Trying
• 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 $Ad{S}_5\times S^5$
• Magnus and Dyson Series for Master Integrals
• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Extension of HPL to complex arguments
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Quantum Gravity from Conformal Field Theory
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• Cuts of Feynman Integrals in Baikov representation
• Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
• Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation
• epsilon: A tool to find a canonical basis of master integrals
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Unmixing Supergravity
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• Conformal Partial Wave Expansions for N=4 Chiral Four Point Functions
• Genus-One String Amplitudes from Conformal Field Theory
• On near forward high energy scattering in QCD
• The double-trace spectrum of N=4 SYM at strong coupling
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• More $\mathcal{N}=4$ superconformal bootstrap
• Landau diagrams in AdS and S-matrices from conformal correlators
• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• String scattering in flat space and a scaling limit of Yang-Mills correlators
• One-loop amplitudes in $Ad{S}_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling
• Unitarity Methods in AdS/CFT
• CFT Unitarity and the AdS Cutkosky Rules
• Higher genus modular graph functions, string invariants, and their exact asymptotics
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Modular properties of two-loop maximal supergravity and connections with string theory
• The Pentabox Master Integrals with the Simplified Differential Equations approach
• Large $p$ explorations. From SUGRA to big STRINGS in Mellin space
• Calculating multiloop integrals using dimensional recurrence relation and D-analyticity
• Simplified differential equations approach for Master Integrals
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM
• Generating series of all modular graph forms from iterated Eisenstein integrals
• Differential equations for loop integrals in Baikov representation
• On Genus-one String Amplitudes on $Ad{S}_5\times S^5$
• One-loop string corrections for AdS Kaluza-Klein amplitudes
• Asymptotics of the $D^8{R}^4$ genus-two string invariant

Cited by in corpus (15)

• Loops in AdS: From the Spectral Representation to Position Space
• One-loop Gluon Amplitudes in AdS
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Generalizing event shapes: In search of lost collider time
• Loops in AdS: From the Spectral Representation to Position Space II
• Towards All Loop Supergravity Amplitudes on $Ad{S}_5\times S^5$
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• AdS super gluon scattering up to two loops: A position space approach
• Notes on gravity multiplet correlators in $Ad{S}_3\times S^3$
• To the cusp and back: Resurgent analysis for modular graph functions
• Positivity, low twist dominance and CSDR for CFTs
• Scattering bound states in AdS
• Non-analytic terms of string amplitudes from partial waves
• Information Geometry and Holographic Correlators
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills