On spinning loop amplitudes in Anti-de Sitter space

Abstract

In this work we present a systematic study of AdS${}_{d+1}$ loop amplitudes for gluons and gravitons using momentum space techniques. Inspired by the recent progress in tree level computation, we construct a differential operator that can act on a scalar factor in order to generate gluon and graviton loop integrands: this systematizes the computation for any given loop level Witten diagram. We then give a general prescription in this formalism, and discuss it for bubble, triangle, and box diagrams.

arXiv comment26 pages, 1 figure

References in corpus (77)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Quantum Contributions to Cosmological Correlations
• The Amplituhedron
• Writing CFT correlation functions as AdS scattering amplitudes
• Implications of conformal invariance in momentum space
• From polygons and symbols to polylogarithmic functions
• A Natural Language for AdS/CFT Correlators
• Spinning AdS Propagators
• Unitarity and the Holographic S-Matrix
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• Loops in AdS from Conformal Field Theory
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• AdS/CFT 4-point functions: How to succeed at z-integrals without really trying
• Bootstrapping Inflationary Correlators in Mellin Space
• On Four-point Functions in the CFT/AdS Correspondence
• Analyticity and the Holographic S-Matrix
• New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators
• Gravitational S-matrix from CFT dispersion relations
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• A Mellin Space Approach to Cosmological Correlators
• Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
• 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
• Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Double copy structure of CFT correlators
• Comments on 4-point functions in the CFT/AdS correspondence
• Conformal $n$-point functions in momentum space
• Renormalised CFT 3-point functions of scalars, currents and stress tensors
• Recursion Relations for AdS/CFT Correlators
• Loop corrections for Kaluza-Klein AdS amplitudes
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• BCFW for Witten Diagrams
• Loops and trees
• Cosmological Polytopes and the Wavefunction of the Universe
• Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3
• Spinning AdS Loop Diagrams: Two Point Functions
• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• Momentum space approach to crossing symmetric CFT correlators
• Unitarity Methods in AdS/CFT
• CFT Unitarity and the AdS Cutkosky Rules
• Evaluation of conformal integrals
• Quantum ${\varphi }^4$ Theory in AdS${}_4$ and its CFT Dual
• Loops in Anti-de Sitter Space
• An étude of momentum space scalar amplitudes in AdS
• All Tree-Level Correlators for M-theory on $Ad{S}_7\times S^4$
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• New relation for AdS amplitudes
• Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension
• Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative $TJJ$ Vertex
• Loops in AdS: From the Spectral Representation to Position Space
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• Towards the higher point holographic momentum space amplitudes II: Gravitons
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• From bulk loops to boundary large-N expansion
• On boundary correlators in Liouville theory on AdS${}_2$
• All-Mass $n$-gon Integrals in $n$ Dimensions
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• Simplicity in AdS Perturbative Dynamics
• $\lambda {\varphi }^4$ in dS
• Tree-level Correlators of scalar and vector fields in AdS/CFT
• On the Emergence of Lorentz Invariance and Unitarity from the Scattering Facet of Cosmological Polytopes
• Polyakov-Mellin Bootstrap for AdS loops
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ III: Contact Four-Point Amplitudes
• Momentum space CFT correlators for Hamiltonian truncation
• Cosmological Polytopes and the Wavefuncton of the Universe for Light States
• From the flat-space S-matrix to the Wavefunction of the Universe
• AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering
• Towards the higher point holographic momentum space amplitudes
• Symbol Recursion for the dS Wave Function
• Recursion Relations in $p$-adic Mellin Space
• 4-point function from conformally coupled scalar in AdS${}_6$
• Loops in the Bulk

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