Geodesic Diagrams, Gravitational Interactions & OPE Structures

Abstract

We give a systematic procedure to evaluate conformal partial waves involving symmetric tensors for an arbitrary CFT${}_d$ using geodesic Witten diagrams in AdS${}_{d+1}$. Using this procedure we discuss how to draw a line between the tensor structures in the CFT and cubic interactions in AdS. We contrast this map to known results using three-point Witten diagrams: the maps obtained via volume versus geodesic integrals differ. Despite these differences, we show how to decompose four-point exchange Witten diagrams in terms of geodesic diagrams, and we discuss the product expansion of local bulk fields in AdS.

arXiv commenttypos corrected, references added

References in corpus (42)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Bounding scalar operator dimensions in 4D CFT
• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning Conformal Correlators
• Conformal Regge theory
• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Spinning Conformal Blocks
• Cubic interaction vertices for massive and massless higher spin fields
• Carving Out the Space of 4D CFTs
• 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
• A Stereoscopic Look into the Bulk
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• A Mellin space approach to the conformal bootstrap
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
• Entanglement, Holography and Causal Diamonds
• Higher-spin Interactions from CFT: The Complete Cubic Couplings
• General Scalar Exchange in AdS_d+1
• Comments on 4-point functions in the CFT/AdS correspondence
• Evaluating the AdS dual of the critical O(N) vector model
• Conformal correlators of mixed-symmetry tensors
• On the cubic interactions of massive and partially-massless higher spins in (A)dS
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• Generating functions of (partially-)massless higher-spin cubic interactions
• Radial expansion for spinning conformal blocks
• Seed Conformal Blocks in 4D CFT
• Harmony of Spinning Conformal Blocks
• Scalar-Vector Bootstrap
• Anatomy of Geodesic Witten Diagrams
• Higher-Spin Algebras, Holography and Flat Space
• Conditions on holographic entangling surfaces in higher curvature gravity
• Geodesic Witten diagrams with an external spinning field
• A note on the analyticity of AdS scalar exchange graphs in the crossed channel
• A Calculus for Higher Spin Interactions

Cited by in corpus (35)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Bootstrapping Inflationary Correlators in Mellin Space
• A Mellin Space Approach to Cosmological Correlators
• Weight Shifting Operators and Conformal Blocks
• From dS to AdS and back
• Spinning AdS Loop Diagrams: Two Point Functions
• Universal Lowest-Twist in CFTs from Holography
• Holographic Entanglement and Poincare blocks in three dimensional flat space
• Simplifying large spin bootstrap in Mellin space
• Holographic dual of the five-point conformal block
• Witten Diagrams for Torus Conformal Blocks
• AdS Weight Shifting Operators
• Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals
• Higher-Point Conformal Blocks in the Comb Channel
• Geodesic bulk diagrams on the Bruhat-Tits tree
• Holographic OPE Coefficients from AdS Black Holes with Matters
• Thermal Conformal Blocks
• A multipoint conformal block chain in $d$ dimensions
• Spinning Geodesic Witten Diagrams
• Seven-Point Conformal Blocks in the Extended Snowflake Channel and Beyond
• Six-Point Conformal Blocks in the Snowflake Channel
• New Methods for Conformal Correlation Functions
• Towards Spinning Mellin Amplitudes
• Towards Feynman rules for conformal blocks
• 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
• Scalar Blocks as Gravitational Wilson Networks
• Feynman rules for higher-spin gauge fields on AdS${}_{d+1}$
• Geodesic Witten diagrams with anti-symmetric exchange
• Efficient Rules for All Conformal Blocks
• Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena
• Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$
• The gravity dual of Lorentzian OPE blocks
• More on Boundary Holographic Witten Diagrams