Spinning AdS Loop Diagrams: Two Point Functions

Abstract

We develop a systematic approach to evaluating AdS loop amplitudes based on the spectral (or "split") representation of bulk-to-bulk propagators, which re-expresses loop diagrams in terms of spectral integrals and higher-point tree diagrams. In this work we focus on 2pt one-loop Witten diagrams involving totally symmetric fields of arbitrary mass and integer spin. As an application of this framework, we study the contribution to the anomalous dimension of higher-spin currents generated by bubble diagrams in higher-spin gauge theories on AdS.

54+23 pages, 15 figures. v2: Section 2.2 added with more details on the analytic evaluation of anomalous dimensions from bubble diagrams. References added, matches published version

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• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning AdS Propagators
• Loops in AdS from Conformal Field Theory
• Conformal Bootstrap in Mellin Space
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• Quantum Gravity from Conformal Field Theory
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Current Exchanges and Unconstrained Higher Spins
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• Spinning Witten Diagrams
• BCFW for Witten Diagrams
• Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions
• (A)dS exchanges and partially-massless higher spins
• Higher-Spin Algebras, Holography and Flat Space
• Anatomy of Geodesic Witten Diagrams
• Geodesic Diagrams, Gravitational Interactions & OPE Structures
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• Flato-Fronsdal theorem for higher-order singletons
• Geodesic bulk diagrams on the Bruhat-Tits tree
• On the Holography of Free Yang-Mills
• Feynman rules for higher-spin gauge fields on AdS${}_{d+1}$
• Geodesic Witten diagrams with anti-symmetric exchange
• Anomalous dimensions of higher spin currents in large N CFTs
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry
• One-Loop Free Energy of Tensionless Type IIB String in AdS${}_5\times$S${}^5$

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