Loop corrections as marginal deformations in celestial holography

The infrared (IR) singularities of four-dimensional all-loop amplitudes for QED and gravity have a universal factorization structure. In celestial holography, these scattering amplitudes are mapped to correlation functions in a celestial conformal field theory (CCFT) residing on a codimension two surface. Here we systematically establish a precise correspondence between the all-loop corrected 4D amplitudes and correlation functions within the CCFT, incorporating corresponding marginal deformations. This provides a holographic interpretation of the IR universal factorization structure of the all-loop amplitudes which extends the celestial dictionary.