# Leaf amplitudes In [[0010 Celestial holography|celestial holography]], scattering amplitudes in 4d flat space are written as correlation functions of a 2d CFT on a sphere called the [[0022 Celestial sphere|celestial sphere]]. One problem with this is that translation invariance in 4d leads to the correlator being distributional. **Leaf amplitudes** are one way out of this. Foliating the bulk using hyperbolic slice, one can compute amplitudes on each slice and sum over them at the end. The distributional nature comes as a result of summation, while each leaf amplitude is regular and smooth. ## Refs - original - [[2023#Melton, Sharma, Strominger (Dec)]] - soft algebra - [[2024#Melton, Sharma, Strominger]] - spectral representation - [[2024#Duary, Maji]] - dual of MHV - [[2024#Melton, Sharma, Strominger, Wang]]