Abstract
We provide necessary and sufficient conditions for a Conformal Field Theory
to have a description in terms of a perturbative Effective Field Theory in AdS.
The first two conditions are well-known: the existence of a perturbative `1/N'
expansion and an approximate Fock space of states generated by a finite number
of low-dimension operators. We add a third condition, that the Mellin
amplitudes of the CFT correlators must be well-approximated by functions that
are bounded by a polynomial at infinity in Mellin space, or in other words,
that the Mellin amplitudes have an effective theory-type expansion. We explain
the relationship between our conditions and unitarity, and provide an analogy
with scattering amplitudes that becomes exact in the flat space limit of AdS.
The analysis also yields a simple connection between conformal blocks and AdS
diagrams, providing a new calculational tool very much in the spirit of the
S-Matrix program.
We also begin to explore the potential pathologies associated with higher
spin fields in AdS by generalizing Weinberg's soft theorems to AdS/CFT. The AdS
analog of Weinberg's argument constrains the interactions of conserved currents
in CFTs, but there are potential loopholes that are unavailable to theories of
massless higher spin particles in flat spacetime.
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