Abstract
S-matrix elements in flat space can be obtained from a large AdS-radius limit of certain CFT correlators. We present a method for constructing CFT operators which create incoming and outgoing scattering states in flat space. This is done by taking the flat limit of bulk operator reconstruction techniques. Using this method, we obtain explicit expressions for incoming and outgoing U(1) gauge fields. Weinberg soft photon theorems then follow from Ward identites of conserved CFT currents. In four bulk dimensions, gauge fields on AdS can be quantized with standard and alternative boundary conditions. Changing the quantization scheme corresponds to the S-transformation of SL(2, ℤ) electric-magnetic duality in the bulk. This allows us to derive both, the electric and magnetic soft photon theorems in flat space from CFT physics.
Highlights
Despite much progress in the understanding of quantum gravity in asymptotically Antide Sitter spaces [1, 2], good insight into a holographic description of gravity in Minkowski space is still elusive
We present a method for constructing CFT operators which create incoming and outgoing scattering states in flat space
In this note we report on results which aim to further clarify the structure of holography in asymptotically flat space-times making use of the large radius limit of AdS/CFT
Summary
Despite much progress in the understanding of quantum gravity in asymptotically Antide Sitter spaces [1, 2], good insight into a holographic description of gravity in Minkowski space is still elusive. We show that for the case of a U(1) gauge theory, Weinberg soft theorems can be understood as arising from Ward identities of a CFT in the strict large N limit. This will give a formula for scattering amplitudes of massive and massless scalars in terms of CFT correlation functions. We reconstruct scattering amplitudes of a theory in asymptotically flat spacetimes from the correlators of a conformal field theory in one lower dimension This task has been the subject of much work in the literature [4,5,6,7, 12, 21]. We will focus on the case of bulk scalar fields, leaving the discussion of gauge theories for section 3
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