Celestial Regge theory

Exploiting the analytic properties of the scattering amplitude, we provide an alternative but equivalent definition of the standard Mellin transform used to obtain celestial correlation functions. From this representation, we identify a celestial dispersion relation that relates the reduced correlation function to the poles and discontinuities of the bulk amplitude. By drawing an analogy with the standard CFT case, we define the celestial Regge limit and identify the relevant celestial CFT data in terms of the partial amplitudes governing the bulk Regge limit.

💡 Research Summary

The paper “Celestial Regge Theory” by Eduardo Casali and Riccardo Giordano Pozzi develops a novel framework for studying scattering amplitudes in flat space through the lens of celestial conformal field theory (CCFT). The authors begin by reviewing the standard construction of celestial correlators: a four‑point massless amplitude A⁽⁴⁾(ω_i, z_i) is Mellin‑transformed over the external energies ω_i to produce a correlator 𝒜⁽⁴⁾(z_i, Δ_i) that transforms covariantly under the Lorentz group SL(2,ℂ), which acts as the global conformal group on the celestial sphere. The correlator factorises into a universal kinematic prefactor K(z_i, \bar z_i) and a reduced function f_{Δ_i,ℓ_i}(z, \bar z) that carries the dynamical information.

The core technical advance is an alternative definition of the Mellin transform, obtained by a contour deformation (“contour trick”) in the complex μ‑plane. This manipulation isolates the contributions from poles (residues) and branch‑cut discontinuities of the bulk amplitude T(s,t). The resulting “celestial dispersion relation” reads

g(β,z)=2^{−3−β}π sin(πβ/2) z² ∑_i Res