Spinning Witten diagrams

2017/02/28 by Charlotte Sleight, Massimo Taronna · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Diagram #Gauge theory #Geometry #Half-integer #Integer (computer science) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Scalar (mathematics) #Spin (aerodynamics) #Spinning #Theoretical physics #Thermodynamics #gr-qc #hep-th

paper · pdf · doi:10.1007/jhep06(2017)100

41 pages, many figures. v2: Three self-contained pages removed from section 4, to be restored elsewhere. Main results unaffected. Refs added and typos fixed

arxiv created 2017/03/02 · openalex publication_date 2017/06/01 · arxiv updated 2017/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop a systematic framework to compute the conformal partial wave expansions (CPWEs) of tree-level four-point Witten diagrams with totally symmetric external fields of arbitrary mass and integer spin in AdS d+1. As an intermediate step, we identify convenient bases of three-point bulk and boundary structures to invert linear map between spinning three-point conformal structures and spinning cubic couplings in AdS. Given a CFT d , this provides the complete holographic reconstruction of all cubic couplings involving totally symmetric fields in the putative dual theory on AdS d+1. Employing this framework, we determine the CPWE of a generic four-point exchange Witten diagram with spinning exchanged field. As a concrete application, we compute all four-point exchange Witten diagrams in the type A higher-spin gauge theory on AdS d+1, which is conjectured to be dual to the free scalar O (N ) model.

Citations

• Entanglement Entropy at Large Central Charge
• Notes On Higher Spin Symmetries
• Conformal Partial Waves: Further Mathematical Results
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• On Massive High Spin Particles in (A)dS
• Virasoro conformal blocks and thermality from classical background fields
• JuliBootS: a hands-on guide to the conformal bootstrap
• High Energy Scattering in the AdS/CFT Correspondence
• AdS box graphs, unitarity and operator product expansions
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• Conformal partial waves and the operator product expansion
• Spinning AdS propagators
• The group approach to AdS space propagators
• Infinite conformal symmetry in two-dimensional quantum field theory
• Massless higher spins and holography
• Gauge boson exchange in AdSd+1
• Correlation functions and massive Kaluza–Klein modes in the AdS/CFT correspondence
• On relativistic wave equations for particles of arbitrary spin in an electromagnetic field
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Evaluating the AdS dual of the criticalO(N) vector model
• A semidefinite program solver for the conformal bootstrap
• Constraining conformal field theories with a higher spin symmetry
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Geometric massive higher spins and current exchanges
• Constraining conformal field theories with a higher spin symmetry in d=4
• Bounds on 4D conformal and superconformal field theories
• Bounding scalar operator dimensions in 4D CFT
• (A)dS exchanges and partially-massless higher spins
• The Large-N Limit of Superconformal Field Theories and Supergravity

Cited by

• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
• Towards a bootstrap approach to higher orders of epsilon expansion
• Simplifying large spin bootstrap in Mellin space
• Geodesic Witten diagrams with antisymmetric tensor exchange