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.

arXiv comment32 + 8 pages, 3 figures

References in corpus (46)

• Comments on the Sachdev-Ye-Kitaev model
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3D Ising Model with the Conformal Bootstrap
• Conformal Partial Waves and the Operator Product Expansion
• Quantum Field Theory in the Large N Limit: a review
• Spinning Conformal Correlators
• Analyticity in Spin in Conformal Theories
• Projectors, Shadows, and Conformal Blocks
• Bootstrapping the O(N) Vector Models
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Spinning Conformal Blocks
• A holographic reduction of Minkowski space-time
• Lectures on Celestial Amplitudes
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• A spacetime derivation of the Lorentzian OPE inversion formula
• Unitarity, stability and loops of unstable ghosts
• Symmetries of Celestial Amplitudes
• Celestial Amplitudes from UV to IR
• A Study of Quantum Field Theories in AdS at Finite Coupling
• A tauberian theorem for the conformal bootstrap
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• Extended BMS Algebra of Celestial CFT
• Crossing Symmetry in Alpha Space
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• Extended Super BMS Algebra of Celestial CFT
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
• Conformal Block Expansion in Celestial CFT
• The Complex-Mass Scheme and Unitarity in perturbative Quantum Field Theory
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• Conformal Blocks from Celestial Gluon Amplitudes
• Primary Fields in Celestial CFT
• A note on the SYK model with complex fermions
• A Crossing-Symmetric OPE Inversion Formula
• Goldilocks Modes and the Three Scattering Bases
• Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
• Relativistic partial waves for celestial amplitudes
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs
• Massive Spinning Bosons on the Celestial Sphere
• Bulk locality from the celestial amplitude
• Celestial Geometry
• Mapping SYK to the Sky

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• Celestial amplitude for 2d theory
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• 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