Flat space physics from AdS/CFT

Abstract

We propose a formula relating scattering S-matrix amplitudes to correlators of a conformal field theory. The proposal implements a flat limit of the field theory, providing an indirect microscopic description of gravitational theories with asymptotically flat boundary conditions. The formula is valid for both massive and massless external particles, and reduces to existing expressions in the literature when all particles are either simultaneously massless or massive. We test the result in various (2+1)-dimensional examples such as simple BMS3 invariant correlators and blocks. We also study two-point correlators in conformal field theory deficit states to obtain known expressions for non-trivial scattering in asymptotically flat conical geometries.

38 pages, 3 figures. Added Fig.2. Journal version

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• Geometric actions and flat space holography
• Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT
• Growing Extra Dimensions in AdS/CFT
• Helicity basis for three-dimensional conformal field theory
• Towards Bootstrapping RG flows: Sine-Gordon in AdS
• On Galilean conformal bootstrap
• Hamiltonian truncation in Anti-de Sitter spacetime
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• Holographic solar systems and hydrogen atoms: non-relativistic physics in AdS and its CFT dual
• The Shadow Formalism of Galilean CFT${}_2$
• Chaos in Celestial CFT
• $1/L^2$ corrected soft photon theorem from a CFT${}_3$ Ward identity
• A Scattering Amplitude for Massive Particles in AdS
• Renormalization group flows in AdS and the bootstrap program
• Soft Photon theorem in the small negative cosmological constant limit
• Flat-space structure of gluon and graviton in AdS
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• Bootstrapping Witten diagrams via differential representation in Mellin space
• Semi-classical BMS-blocks from the Oscillator Construction
• Radiation in Fluid/Gravity and the Flat Limit
• A Carroll Limit of AdS/CFT: A Triality with Flat Space Holography?
• $p$-Form Surface Charges on AdS: Renormalization and Conservation
• BMS Symmetry via AdS/CFT
• Spinning Particle Geometries in AdS${}_3$/CFT${}_2$
• 1d Conformal Field Theory and Dispersion Relations
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
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• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Probing multi-particle unitarity with the Landau equations
• Finite-coupling spectrum of O(N) model in AdS
• Nonperfect Carrollian Fluids Through Holography