On the definition of Carrollian amplitudes in general dimensions

TL;DR

This paper refines the definition of Carrollian amplitudes across various dimensions, linking them to scattering matrices and exploring their transformation properties and symmetries.

Contribution

It provides a comprehensive definition of Carrollian amplitudes in general dimensions using vielbein fields and relates them to scattering matrices via a modified Fourier transform.

Findings

Carrollian amplitude defined in general dimensions using vielbein fields

Relation established between Carrollian amplitude and scattering matrix

Identified isomorphism between local rotations and superduality transformations

Abstract

Carrollian amplitude is the natural object that defines the correlator of the boundary Carrollian field theory. In this work, we will elaborate on its proper definition in general dimensions. We use the vielbein field on the unit sphere to define the fundamental field with non-vanishing helicity in the local Cartesian frame which is the building block of the Carrollian amplitude. In general dimensions, the Carrollian amplitude is related to the momentum space scattering matrix by a modified Fourier transform. The Poincar\'e transformation law of the Carrollian amplitude in this definition has been discussed. We also find an isomorphism between the local rotation of the vielbein field and the superduality transformation.