Massive carrollian fields at timelike infinity

TL;DR

This paper explores the relationship between massive fields in Minkowski space near timelike infinity and their description as massive carrollian fields on a specific geometric structure, revealing connections to holography, symmetries, and scattering amplitudes.

Contribution

It constructs the framework for describing massive fields as carrollian fields on 4i, establishes a dictionary linking these to Minkowski and celestial basis fields, and discusses implications for holography and scattering amplitudes.

Findings

Massive fields near timelike infinity can be described as massive carrollian fields.

The symmetries of the carrollian structure explain BMS charges and soft theorems.

A preliminary link between scattering amplitudes and carrollian correlation functions is proposed.

Abstract

Motivated by flat space holography, we demonstrate that massive spin-$s$ fields in Minkowski space near timelike infinity are massive carrollian fields on the carrollian counterpart of anti-de Sitter space called $\mathsf{Ti}$. Its isometries form the Poincar\'e group, and we construct the carrollian spin-$s$ fields using the method of induced representations. We provide a dictionary between massive carrollian fields on $\mathsf{Ti}$ and massive fields in Minkowski space, as well as to fields in the conformal primary basis used in celestial holography. We show that the symmetries of the carrollian structure naturally account for the BMS charges underlying the soft graviton theorem. Finally, we initiate a discussion of the correspondence between massive scattering amplitudes and carrollian correlation functions on $\mathsf{Ti}$, and introduce physical definitions of detector operators using a suitable notion of conserved carrollian energy-momentum tensor.