Bulk locality from the celestial amplitude

TL;DR

This paper explores how bulk locality in quantum field theories influences celestial amplitudes, revealing their structure through partial wave expansions and dispersion relations, with applications to string theory amplitudes.

Contribution

It establishes a connection between bulk locality and the imaginary part of celestial amplitudes, deriving celestial dispersion relations and expanding Poincaré partial waves in terms of 2D conformal partial waves.

Findings

Imaginary part of celestial amplitude reflects bulk S-matrix factorization.

Derived celestial dispersion relation linking imaginary part and residues.

Explicitly expanded Poincaré partial waves in 2D conformal partial waves.

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 Poincar\'e 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 Poincar\'e partial waves in terms of 2D conformal partial waves.