Spinning Witten Diagrams

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${}_{d+1}$. Employing this framework, we determine the CPWE of a generic exchange Witten diagram with spinning exchanged field. As an intermediate step, we diagonalise the linear map between spinning three-point conformal structures and spinning cubic couplings in AdS. As a concrete application, we compute all exchange diagrams in the type A higher-spin gauge theory on AdS${}_{d+1}$, which is conjectured to be dual to the free scalar $O\left(N\right)$ model. Given a CFT${}_d$, our results provide the complete holographic reconstruction of all cubic couplings involving totally symmetric fields in the putative dual theory on AdS${}_{d+1}$.

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

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Cited by in corpus (62)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Bootstrapping Inflationary Correlators in Mellin Space
• The Bulk Dual of SYK: Cubic Couplings
• A Mellin Space Approach to Cosmological Correlators
• All point correlation functions in SYK
• Weight Shifting Operators and Conformal Blocks
• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• From dS to AdS and back
• Higher-Spin Gauge Theories and Bulk Locality
• Dispersive CFT Sum Rules
• On duality of color and kinematics in (A)dS momentum space
• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• Spinning AdS Loop Diagrams: Two Point Functions
• Momentum space approach to crossing symmetric CFT correlators
• Unitarity Methods in AdS/CFT
• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
• Holographic dual of the five-point conformal block
• Simplifying large spin bootstrap in Mellin space
• Anatomy of Geodesic Witten Diagrams
• Witten Diagrams for Torus Conformal Blocks
• Anomalous Dimensions from Crossing Kernels
• Cubic interactions for arbitrary spin N-extended massless supermultiplets in 4d flat space
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• AdS Weight Shifting Operators
• Higher-Point Conformal Blocks in the Comb Channel
• Chern-Simons Matter Theories and Higher Spin Gravity
• Geodesic bulk diagrams on the Bruhat-Tits tree
• Spinning conformal defects
• A multipoint conformal block chain in $d$ dimensions
• Spinning Geodesic Witten Diagrams
• Double-Trace Deformations of Conformal Correlations
• Seven-Point Conformal Blocks in the Extended Snowflake Channel and Beyond
• Six-Point Conformal Blocks in the Snowflake Channel
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• Tensors and Spinors in de Sitter Space
• New Methods for Conformal Correlation Functions
• Towards Spinning Mellin Amplitudes
• Model-Dependence of Minimal-Twist OPEs in $d>2$ Holographic CFTs
• Towards Feynman rules for conformal blocks
• Operator product expansion for conformal defects
• Fermions in Geodesic Witten Diagrams
• On conformal correlators and blocks with spinors in general dimensions
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Feynman rules for higher-spin gauge fields on AdS${}_{d+1}$
• Geodesic Witten diagrams with anti-symmetric exchange
• Efficient Rules for All Conformal Blocks
• All plus four point (A)dS graviton function using generalized on-shell recursion relation
• Mellin-(Schwinger) representation of One-loop Witten diagrams in AdS
• Conformal partial waves in momentum space
• Constraints for Three-Dimensional Higher-Spin Interactions and Conformal Correlators
• Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena
• Restrictions for $n$-Point Vertices in Higher-Spin Theories
• Higher spin fluctuations on spinless 4D BTZ black hole
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$
• Character Integral Representation of Zeta function in AdS${}_{d+1}$: II. Application to partially-massless higher-spin gravities
• A note on higher-order vertices of higher-spin fields in flat and (A)dS space
• The gravity dual of Lorentzian OPE blocks
• Spinors and conformal correlators
• All Global One- and Two-Dimensional Higher-Point Conformal Blocks
• Deeply Virtual Compton Scattering in Improved Holographic QCD
• Analytic Studies of Fermions in the Conformal Bootstrap