Abstract
We introduce Mellin amplitudes for correlation functions of k scalar operators and one operator with spin in conformal field theories (CFT) in general dimension. We show that Mellin amplitudes for scalar operators have simple poles with residues that factorize in terms of lower point Mellin amplitudes, similarly to what happens for scattering amplitudes in flat space. Finally, we study the flat space limit of Anti-de Sitter (AdS) space, in the context of the AdS/CFT correspondence, and generalize a formula relating CFT Mellin amplitudes to scattering amplitudes of the bulk theory, including particles with spin.
Highlights
We introduce Mellin amplitudes for correlation functions of k scalar operators and one operator with spin in conformal field theories (CFT) in general dimension
We show that Mellin amplitudes for scalar operators have simple poles with residues that factorize in terms of lower point Mellin amplitudes, to what happens for scattering amplitudes in flat space
Mellin amplitudes are an alternative representation of conformal correlation functions that are analogous to scattering amplitudes
Summary
Mellin amplitudes are an alternative representation of conformal correlation functions that are analogous to scattering amplitudes. We shall show that the Operator Product Expansion (OPE) leads to the factorization of the residues of the poles of Mellin amplitudes. As explained in [3] (section 2.1), for each primary operator Op, with dimension ∆ and spin J, that appears in the OPE (1.1), the Mellin amplitude has an infinite sequence of poles. K a=1 pa approaches the mass shell, p2 + M 2 = 0, of a particle in the theory The residue of this pole factorizes in terms of lower point scattering amplitudes.
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