Ambitwistor strings at null infinity and subleading soft limits

TL;DR

This paper explores the connection between BMS symmetries at null infinity, soft theorems, and ambitwistor string theory, providing a geometric and string-theoretic framework for understanding gravitational scattering and symmetries.

Contribution

It develops a novel approach linking ambitwistor string theory with BMS symmetries and soft theorems, including subleading terms, in a unified geometric setting.

Findings

BMS symmetries lift to Hamiltonian actions on ambitwistor space.

Vertex operators generate diffeomorphisms corresponding to soft theorems.

Explicit correspondence between null geodesic scattering and gravitational fields.

Abstract

The relationships between extended BMS symmetries at null infinity and Weinberg's soft theorems for gravitons and photons together with their subleading generalizations are developed using ambitwistor string theory. Ambitwistor space is the phase space of complex null geodesics in complexified space-time. We show how it can be canonically identified with the cotangent bundle of null infinity. BMS symmetries of null infinity lift to give a hamiltonian action on ambitwistor space, both in general dimension and in its twistorial 4-dimensional representation. General vertex operators arise from hamiltonians generating diffeomorphisms of ambitwistor space that determine the scattering from past to future null infinity. When a momentum eigenstate goes soft, the diffeomorphism defined by its leading and its subleading part are extended BMS generators realized in the world sheet conformal field theory of the ambitwistor string. More generally, this gives explicit perturbative correspondence between the scattering of null geodesics and that of the gravitational field via ambitwistor string theory.