$1/L^2$ corrected soft photon theorem from a CFT${}_3$ Ward identity

Abstract

Classical soft theorems applied to probe scattering processes on AdS${}_4$ spacetimes predict the existence of $1/L^2$ corrections to the soft photon and soft graviton factors of asymptotically flat spacetimes. In this paper, we establish that the $1/L^2$ corrected soft photon theorem can be derived from a large $N$ CFT${}_3$ Ward identity. We derive a perturbed soft photon mode operator on a flat spacetime patch in global AdS${}_4$ in terms of an integrated expression of the boundary CFT current. Using the same in the CFT${}_3$ Ward identity, we recover the $1/L^2$ corrected soft photon theorem derived from classical soft theorems.

32 pages, 1 figure

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• Writing CFT correlation functions as AdS scattering amplitudes
• Holographic representation of local bulk operators
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• New symmetries for the Gravitational S-matrix
• Low's Subleading Soft Theorem as a Symmetry of QED
• Local bulk S-matrix elements and CFT singularities
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• Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• de Sitter corrections to supertranslation Ward identity and soft graviton theorem