Celestial Conformal Primaries in Effective Field Theories

Scattering amplitudes in $d+2$ dimensions can be recast as correlators of conformal primary operators in a putative holographic CFTd by working in a basis of boost eigenstates instead of momentum eigenstates. It has been shown previously that conformal primary operators with Δ ∈ d/2 + i R form a basis for massless one-particle representations. In this paper, we consider more general conformal primary operators with Δ ∈ C and show that completeness, normalizability, and consistency with CPT implies that we must restrict the scaling dimensions to either Δ ∈ d/2 + i R or Δ ∈ R. Unlike those with Δ ∈ d/2 + i R, the conformal primaries with Δ ∈ R can be constructed without knowledge of the UV and can therefore be defined in effective field theories. With additional analyticity assumptions, we can restrict Δ ∈ 2 - Z≥0 or Δ ∈ 1/2- Z≥0 for bosonic or fermionic operators, respectively.