Spinning AdS propagators

2014/04/22 by Miguel S. Costa, Vasco Gonçalves, Vasco Goncalves +2 · 1 voice · 8 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Cosmology and Gravitation Theories #Embedding #Formalism (music) #Gravitation #Graviton #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Propagator #Quantum electrodynamics #Quantum mechanics #Theoretical physics #hep-th

paper · pdf · doi:10.1007/jhep09(2014)064

48 pages, 6 figures

arxiv created 2014/04/22 · arxiv published 2014/04/22 · arxiv updated 2014/04/22 · openalex publication_date 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop the embedding formalism to describe symmetric traceless tensors in Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk propagator of massive spin J fields and check that it has the expected short distance and massless limits. We also find a split representation for the bulk-to-bulk propagator, by writing it as an integral over the boundary of the product of two bulk-to-boundary propagators. We exemplify the use of this representation with the computation of the conformal partial wave decomposition of Witten diagrams. In particular, we determine the Mellin amplitude associated to AdS graviton exchange between minimally coupled scalars of general dimension, including the regular part of the amplitude.

Citations

• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Conformal Partial Waves: Further Mathematical Results
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• High Energy Scattering in the AdS/CFT Correspondence
• The group approach to AdS space propagators
• On relativistic wave equations for particles of arbitrary spin in an electromagnetic field
• Implications of Conformal Invariance in Field Theories for General Dimensions
• (A)dS exchanges and partially-massless higher spins
• The Large-N Limit of Superconformal Field Theories and Supergravity
• The large N limit of superconformal field theories and supergravity

Cited by

• UV-finite “old” conformal bootstrap on AdS: scalar case
• Spinning Witten diagrams
• Towards a bootstrap approach to higher orders of epsilon expansion
• Anomalous dimensions from thermal AdS partition functions
• The unique Polyakov blocks
• Simplifying large spin bootstrap in Mellin space
• Geodesic Witten diagrams with antisymmetric tensor exchange
• Spinning loop amplitudes in anti–de Sitter space

Discussions

• You may be familiar with a good reference for the embedding space in AdS. It defines chordal distance in a way which is exactly $-1/2$ of what you wrote. \begin{align} u &= \frac{1}{2} (X_1 - X_2)^2 \ [stackexchange, 0 points]

Related

• A Bispinor Formalism for Spinning Witten Diagrams
• Spinning Fields in Lorentzian AdS
• CFT adapted gauge invariant formulation of massive arbitrary spin fields in AdS
• Spinning Mellin amplitudes
• Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange