Notes on Resonances and Unitarity from Celestial Amplitudes

Abstract

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.

32 + 8 pages, 3 figures

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• Celestial amplitudes in an ambidextrous basis
• Integrable Field Theories and Their CCFT Duals
• Celestial amplitude for 2d theory
• Celestial Mellin Amplitude
• A General Hierarchy of Charges at Null Infinity via the Todd Polynomials
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle