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Ambitwistor strings at null infinity and subleading soft limits

Yvonne Geyer, Arthur E. Lipstein, Lionel Mason

TL;DR

Ambitwistor-string theory provides a geometric bridge between null infinity and scattering amplitudes by identifying ambitwistor space with the cotangent bundle of null infinity, $\mathbb{A}=T^*\mathscr{I}$, and lifting BMS symmetries to act canonically on this space.Expanding graviton and gauge-field vertex operators in soft momentum reveals leading and subleading contributions that generate Supertranslations and Superrotations on $\mathscr{I}$, manifesting Weinberg’s soft theorems as Ward identities within the worldsheet CFT, with higher-order terms corresponding to broader diffeomorphisms of $\mathbb{A}$.The paper develops both general-dimension and four-dimensional twistorial ambitwistor-string models, showing they reproduce known soft theorems (and, in 4d, connect to the Adamo–Casali–Skinner framework) and yield CHY-type formulations for tree amplitudes, while outlining avenues for nonlinear and loop extensions.Overall, the work provides a unifying, geometric perspective on infrared structure of gauge and gravitational theories through diffeomorphisms of ambitwistor space and its relation to null infinity.

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.

Ambitwistor strings at null infinity and subleading soft limits

TL;DR

Ambitwistor-string theory provides a geometric bridge between null infinity and scattering amplitudes by identifying ambitwistor space with the cotangent bundle of null infinity, $\mathbb{A}=T^*\mathscr{I}$, and lifting BMS symmetries to act canonically on this space.Expanding graviton and gauge-field vertex operators in soft momentum reveals leading and subleading contributions that generate Supertranslations and Superrotations on $\mathscr{I}$, manifesting Weinberg’s soft theorems as Ward identities within the worldsheet CFT, with higher-order terms corresponding to broader diffeomorphisms of $\mathbb{A}$.The paper develops both general-dimension and four-dimensional twistorial ambitwistor-string models, showing they reproduce known soft theorems (and, in 4d, connect to the Adamo–Casali–Skinner framework) and yield CHY-type formulations for tree amplitudes, while outlining avenues for nonlinear and loop extensions.Overall, the work provides a unifying, geometric perspective on infrared structure of gauge and gravitational theories through diffeomorphisms of ambitwistor space and its relation to null infinity.

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.

Paper Structure

This paper contains 18 sections, 112 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Ambitwistor strings at null infinity
  3. Background geometry
  4. BMS symmetries and their generalizations
  5. The string model
  6. Symmetries, vertex operators and diffeomorphisms
  7. From soft limits to BMS
  8. Four dimensional ambitwistor strings at $\mathscr{I}$
  9. Symmetries and hamiltonians
  10. The string model
  11. Soft limits
  12. Brief comparison to the model of Adamo et. al.
  13. Conclusion and discussion
  14. Details of the correlators with soft limits
  15. Yang-Mills soft limits in $d$-dimensional model
  16. ...and 3 more sections

Figures (1)

  • Figure 1: Diagram of null infinity, $\mathscr{I}$.