Notes on flat-space limit of AdS/CFT

Abstract

Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $⟨VV\mathcal{O}⟩$ maps to photon-photon-massive amplitudes.

57 pages, 12 figures, latex; comments added, refs added; the version to appear on JHEP

References in corpus (18)

• New Relations for Gauge-Theory Amplitudes
• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Holographic representation of local bulk operators
• Flat Holography: Aspects of the dual field theory
• Gluon Amplitudes as 2d Conformal Correlators
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Local bulk S-matrix elements and CFT singularities
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Gluon Scattering in AdS from CFT
• On duality of color and kinematics in (A)dS momentum space
• Color/Kinematics Duality in AdS${}_4$
• String scattering in flat space and a scaling limit of Yang-Mills correlators
• All Tree-Level Correlators for M-theory on $Ad{S}_7\times S^4$
• D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models
• Double copy structure of parity-violating CFT correlators
• Distributions in CFT II. Minkowski Space
• Dispersion Formulas in QFTs, CFTs, and Holography

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