# Conformally Soft Theorem in Gauge Theory

## TL;DR

This paper demonstrates that celestial gluon scattering at tree level obeys conformally soft theorems involving conformal weights approaching zero, revealing a new aspect of soft behavior in celestial amplitudes beyond traditional energy-based soft theorems.

## Contribution

It introduces conformally soft theorems in celestial gauge theory, showing their validity at tree level and their independence from low-energy effective field theory derivations.

## Key findings

- Celestial gluon scattering obeys conformally soft theorems at tree level.
- Conformally soft theorems involve conformal weights approaching zero.
- These theorems are not derivable from standard low-energy effective theories.

## Abstract

Asymptotic particle states in four-dimensional celestial scattering amplitudes are labelled by their $SL(2,\mathbb{C})$ Lorentz/conformal weights $(h,\bar{h})$ 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 $h \to 0$ or $\bar{h} \to 0$. Unlike the energetically soft theorem, the conformally soft theorem cannot be derived from low-energy effective field theory.