Conformally Soft Theorem in Gauge Theory

Asymptotic particle states in four-dimensional celestial scattering amplitudes are labeled by their SL(2, C) Lorentz/conformal weights (h, (h) over bar) rather than the usual energy-momentum four-vector. These boost eigenstates involve a superposition of all energies. As such, celestial gluon (or photon) scattering cannot obey the usual (energetically) soft theorems. In this paper we show that tree-level celestial gluon scattering, in theories with sufficiently soft UV behavior, instead obeys conformally soft theorems involving h -> 0 or (h) over bar -> 0. Unlike the energetically soft theorem, the conformally soft theorem cannot be derived from low-energy effective field theory.