Bulk locality from the celestial amplitude

Abstract

In this paper, we study the implications of bulk locality on the celestial amplitude. In the context of the four-point amplitude, the fact that the bulk S-matrix factorizes locally in poles of Mandelstam variables is reflected in the imaginary part of the celestial amplitude. In particular, on the real axis in the complex plane of the boost weight, the imaginary part of the celestial amplitude can be given as a positive expansion on the Poincaré partial waves, which are nothing but the projection of flat-space spinning polynomials onto the celestial sphere. Furthermore, we derive the celestial dispersion relation, which relates the imaginary part to the residue of the celestial amplitude for negative even integer boost weight. The latter is precisely the projection of low energy EFT coefficients onto the celestial sphere. We demonstrate these properties explicitly on the open and closed string celestial amplitudes. Finally, we give an explicit expansion of the Poincaré partial waves in terms of 2D conformal partial waves.

arXiv comment43 pages, 10 figures. v2: typos corrected, minor clarifications added, SciPost published version

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• Shadow Celestial Amplitude
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Celestial Geometry
• Celestial insights into the S-matrix bootstrap
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
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• Celestial OPE blocks
• A Note on the Analytic Structure of Celestial Amplitudes
• Celestial Holography
• Celestial Regge theory
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle