Holographic Carrollian Currents for Massless Scattering

TL;DR

This paper connects Carrollian conformal field theory at null infinity with soft graviton theorems in massless scattering, revealing a deep algebraic structure and local stress tensor components in twistor space.

Contribution

It demonstrates that Ward identities of Carrollian CFT stress tensors reproduce soft graviton theorems and constructs currents satisfying the $Lw_{1+ abla}$ algebra, linking boundary symmetries to bulk scattering.

Findings

Ward identities reproduce leading and subleading soft graviton theorems.

Stress tensor components are expressed in terms of bulk radiative modes and are local in twistor potentials.

Carrollian CFT currents satisfy the $Lw_{1+ abla}$ algebra and encode soft and collinear scattering limits.

Abstract

We show that the Ward identities of a Carrollian CFT stress tensor at null infinity reproduce the leading and subleading soft graviton theorems for massless scattering in the bulk. We deduce the expressions of the stress tensor components in terms of the bulk radiative modes, and these components turn out to be local at $\mathscr{I}$ in terms of the twistor potentials. This analysis makes the correspondence between the large-time limit of Carrollian amplitudes and the soft limit of momentum space amplitudes manifest. We then construct Carrollian CFT currents from the ascendants of the hard graviton operator, which satisfy the $Lw_{1+\infty}$ algebra. We show that the large-time limit of their Ward identities implies an infinite tower of projected soft graviton theorems in the bulk, while their finite-time OPEs encode the collinear limit of scattering amplitudes.