Celestial Mellin Amplitude

TL;DR

This paper introduces celestial Mellin amplitudes, a new transform in celestial holography, revealing operator dimensions and OPE coefficients in 3D flat spacetime CCFT, and discusses potential higher-dimensional generalizations.

Contribution

It defines celestial Mellin amplitudes for scalar fields in 3D flat spacetime and explores their properties, including the Mellin block expansion and relation to OPE data.

Findings

Poles encode scaling dimensions of exchanged operators.

Residues relate to OPE coefficient squares.

Comparison with inversion formulae highlights consistency.

Abstract

Celestial holography provides a promising avenue to studying bulk scattering in flat spacetime from the perspective of boundary celestial conformal field theory (CCFT). A key ingredient in connecting the two sides is the celestial amplitude, which is given by the Mellin transform of momentum space scattering amplitude in energy. As such, celestial amplitudes can be identified with the correlation functions in celestial conformal field theory. In this paper, we introduce the further notion of celestial Mellin amplitude, which is given by the Mellin transform of celestial amplitude in coordinate. For technical reasons, we focus on the celestial Mellin amplitudes for scalar fields in three dimensional flat spacetime dual to 1D CCFT, and discuss the celestial Mellin block expansion. In particular, the poles of the celestial Mellin amplitude encode the scaling dimensions of the possible exchanged operators, while the residues there are related to the OPE coefficient squares in a linear and explicit way. We also compare the celestial Mellin amplitudes with the coefficient functions which can be obtained using inversion formulae. Finally, we make some comments about the possible generalizations of celestial Mellin amplitudes to higher dimensions.