Unitarity Methods in AdS/CFT

Abstract

We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of arXiv:1612.03891 that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams -- we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams -- in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout.

43+17 pages. v2: fixed typos, treatment of double-ladder

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Cited by in corpus (46)

• From dS to AdS and back
• From Locality and Unitarity to Cosmological Correlators
• The Inflationary Wavefunction from Analyticity and Factorization
• On duality of color and kinematics in (A)dS momentum space
• CFT Unitarity and the AdS Cutkosky Rules
• Bootstrapping Large Graviton non-Gaussianities
• From Amplitudes to Contact Cosmological Correlators
• An étude of momentum space scalar amplitudes in AdS
• Notes on flat-space limit of AdS/CFT
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• Lightcone Bootstrap at higher points
• Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions
• Weak Gravity Conjecture from Conformal Field Theory: A Challenge from Hyperscaling Violating and Kerr-Newman-AdS Black Holes
• On spinning loop amplitudes in Anti-de Sitter space
• Recursion relations for 5-point conformal blocks
• Helicity basis for three-dimensional conformal field theory
• Dispersion Formulas in QFTs, CFTs, and Holography
• Towards Bootstrapping RG flows: Sine-Gordon in AdS
• All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT
• Tensors and Spinors in de Sitter Space
• Opacity from Loops in AdS
• Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals
• Model-Dependence of Minimal-Twist OPEs in $d>2$ Holographic CFTs
• Towards Feynman rules for conformal blocks
• On Holography in General Background and the Boundary Effective Action from AdS to dS
• Loops in AdS: From the Spectral Representation to Position Space II
• Towards All Loop Supergravity Amplitudes on $Ad{S}_5\times S^5$
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ III: Contact Four-Point Amplitudes
• Effective Field Theory in AdS: Continuum Regime, Soft Bombs, and IR Emergence
• AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering
• Bulk renormalization and the AdS/CFT correspondence
• The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop
• Dimensional reduction of higher-point conformal blocks
• Cosmological cutting rules for Bogoliubov initial states
• More on Wilson toroidal networks and torus blocks
• Boundary correlators in WZW model on AdS${}_2$
• Bootstrapping Witten diagrams via differential representation in Mellin space
• Holographic S-fold theories at one loop
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
• Anomalous Dimensions from Thermal AdS Partition Functions
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
• Spinors and conformal correlators
• Information Geometry and Holographic Correlators
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes
• Composite AdS geodesics for CFT correlators and timelike entanglement entropy