  In this paper, we study celestial amplitudes of Goldstone bosons and
conformal soft theorems. Motivated by the success of soft bootstrap in momentum
space and the important role of the soft limit behavior of tree-level
amplitudes, our goal is to extend some of the methods to the celestial sphere.
The crucial ingredient of the calculation is the Mellin transformation, which
transforms four-dimensional scattering amplitudes to correlation functions of
primary operators in the celestial CFT. The soft behavior of the amplitude is
then translated to the singularities of the correlator. Only for amplitudes in
"UV completed theories" (with sufficiently good high energy behavior) the
Mellin integration can be properly performed. In all other cases, the celestial
amplitude is only defined in a distributional sense with delta functions. We
provide many examples of celestial amplitudes in UV-completed models, including
linear sigma models and Z-theory, which is a certain completion of the SU(N)
non-linear sigma model. We also comment on the BCFW-like and soft recursion
relations for celestial amplitudes and the extension of soft bootstrap ideas.
