  We study the celestial description of the $O(N)$ sigma model in the large $N$
limit as introduced by Coleman, Jackiw and Politzer. Focusing on three
dimensions, we analyze the implications of a UV complete, all-loop order
4-point amplitude of pions in terms of correlation functions defined on the
celestial circle. We find these retain many key features from the previously
studied tree-level case, such as their relation to Generalized Free Field
theories and crossing-symmetry, but also incorporate new properties such as
IR/UV softness and S-matrix metastable states. In particular, to understand
unitarity, we propose a form of the optical theorem that controls the imaginary
part of the correlator based solely on the presence of these resonances. We
also explicitly analyze the conformal block expansions and factorization of
four-point functions into three-point functions. We find that summing over
resonances is key for these factorization properties to hold. We end with some
topics for future study.
