Notes on resonances and unitarity from celestial amplitudes
Diego García-Sepúlveda (Kadanoff Center for Theoretical Physics & Enrico Fermi Institute, University of Chicago, Chicago, USA); Alfredo Guevara (Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA, 02138, USA, Black Hole Initiative, Harvard University, Cambridge, MA, 02138, USA, Society of Fellows, Harvard University, Cambridge, MA, 02138, USA); Justin Kulp (Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada, Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada); Jingxiang Wu (Mathematical Institute, University of Oxford, Andrew-Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK)
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.
